M. DRIHEM Douadi

Prof

Directory of teachers

Department

Mathematics Department

Research Interests

Harmonic Analysis, Function Spaces, EDP's

Contact Info

University of M'Sila, Algeria

Email : douadi.drihem@univ-msila.dz

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Recent Publications

2023-12-31

Complex interpolation of function spaces with general weights

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Citation

M. DRIHEM Douadi, (2023-12-31), "Complex interpolation of function spaces with general weights", [national] Commentationes Mathematicae Universitatis Carolinae , Faculty of Mathematics and Physics of Charles University, Prague, Czech Republic.

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2023-06-19

Nemytzkij operators on function spaces of power weights and applications

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Citation

M. DRIHEM Douadi, (2023-06-19), "Nemytzkij operators on function spaces of power weights and applications", [international] 45th Summer Symposium in Real Analysis , Italy

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2023-06-01

Multiplication on Besov and Triebel-Lizorkin spaces of power weights

This paper is concerned with proving some embeddings of the form%
\begin{equation*}
A_{p_{1},q_{1}}^{s}(\mathbb{R}^{n},|\cdot |^{\alpha })\cdot
A_{p_{2},q_{2}}^{r}(\mathbb{R}^{n},|\cdot |^{\alpha })\hookrightarrow
A_{p,q_{1}}^{s}(\mathbb{R}^{n},|\cdot |^{\alpha }).
\end{equation*}%
The different embeddings obtained here are under certain restrictions on the parameters. Here $A_{p,q}^{s}(\mathbb{R}^{n},|\cdot |^{\alpha })$ stands for either the Besov space $B_{p,q}^{s}(\mathbb{R}^{n},|\cdot |^{\alpha })$ or the Triebel-Lizorkin space $F_{p,q}^{s}(\mathbb{R}^{n},|\cdot |^{\alpha })$. These spaces unify and generalize classical Lebesgue spaces of power weights, Sobolev spaces of power weights, Besov spaces and Triebel-Lizorkin spaces. Almost all our assumptions on $s,r,p_{1},p_{2},q_{1}$ and $q_{2}$ are necessary. An application to the continuity of pseudodifferential operators with non-regular symbols on Triebel-Lizorkin spaces of power weights is given.
Citation

M. DRIHEM Douadi, (2023-06-01), "Multiplication on Besov and Triebel-Lizorkin spaces of power weights", [national] Funct. Approx. Comment. Math , Project Euclid

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2023-01-01

Caffarelli–Kohn–Nirenberg inequalities for Besov and Triebel–Lizorkin-type spaces.

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Citation

M. DRIHEM Douadi, (2023-01-01), "Caffarelli–Kohn–Nirenberg inequalities for Besov and Triebel–Lizorkin-type spaces.", [national] Eurasian Mathematical Journal, , L. N. Gumilyov Eurasian National University

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2023

Continuous characterization of the Besov spaces of variable smoothness and integrability

We obtain new equivalent quasinorms of the Besov spaces of variable smoothness and integrability. Our main tools are the continuous version of the Calderón reproducing formula, maximal inequalities, and the variable-exponent technique; however, allowing the parameters to vary from point to point leads to additional difficulties which, in general, can be overcome by imposing regularity assumptions on these exponents.
Citation

M. DRIHEM Douadi, (2023), "Continuous characterization of the Besov spaces of variable smoothness and integrability", [national] Ukrains’kyi Matematychnyi Zhurnal , Springer

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Weak Type Estimate of Singular Integral Operators on Variable Weak Herz-Type Hardy Spaces

This paper is concerned with the boundedness properties of singular integral operators on variable weak Herz spaces and variable weak Herz-type Hardy spaces. Allowing our parameters to vary from point to point will raise extra difficulties, which, in general, are overcome by imposing regularity assumptions on these exponents, either at the origin or at infinity. Our results cover the classical results on weak Herz-type Hardy spaces with fixed exponents.
Citation

M. DRIHEM Douadi, (2023), "Weak Type Estimate of Singular Integral Operators on Variable Weak Herz-Type Hardy Spaces", [national] Armenian Journal of Mathematics , Republic of Armenia National Academy of Sciences

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Spline Representations of Lizorkin–Triebel Spaces with General Weights

In this paper we introduce some new Lizorkin–Triebel type spaces of variable smoothness. Here the smoothness lies in a new weighted class. We give some equivalent quasinorms and their characterizations via oscillations. We show that the box splines and tensor-products of B-splines are suitable to obtain the stable representations of functions of these spaces.
Citation

M. DRIHEM Douadi, (2023), "Spline Representations of Lizorkin–Triebel Spaces with General Weights", [national] Siberian Mathematical Journal , Springer

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Triebel–Lizorkin spaces with general weights

In this paper, the author introduces Triebel–Lizorkin spaces with general smoothness. We present the φ -transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. Also, we establish the smooth atomic and molecular decomposition of these function spaces. To do these we need a generalization of some maximal inequality to the case of general weights.
Citation

M. DRIHEM Douadi, (2023), "Triebel–Lizorkin spaces with general weights", [national] Advances in Operator Theory , Springer

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Besov spaces with general weights.

We introduce Besov spaces with general smoothness. These spaces unify and generalize the classical Besov spaces. We establish the φ-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. We establish the smooth atomic, molecular and wavelet decomposition of these function spaces. A characterization of these function spaces in terms of the difference relations is given.
Citation

M. DRIHEM Douadi, (2023), "Besov spaces with general weights.", [national] J. Math. Study , Global Science Press

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Commutator estimates for vector fields on variable Triebel–Lizorkin spaces

In this paper we present a bilinear estimate for commutators on Triebel–Lizorkin spaces with variable smoothness and integrability, and under no vanishing assumptions on the divergence of vector fields.
Citation

M. DRIHEM Douadi, (2023), "Commutator estimates for vector fields on variable Triebel–Lizorkin spaces", [national] Rendiconti del Circolo Matematico di Palermo Series 2 , Springer

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2022

Variable Besov-type Spaces

In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the φ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces. Moreover the Sobolev embeddings for these function spaces are obtained.
Citation

M. DRIHEM Douadi, (2022), "Variable Besov-type Spaces", [national] Acta Mathematica Sinica, English Series , Springer

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Nemytzkij operators on Sobolev spaces with power weights: I

Let G:R→R be a continuous function. In this paper, we present necessary and sufficient conditions on G such that

{G(f):f∈Wmp(Rn,|⋅|α)}⊂Wmp(Rn,|⋅|α)
holds, with some suitable assumptions on m, α and p.
Citation

M. DRIHEM Douadi, (2022), "Nemytzkij operators on Sobolev spaces with power weights: I", [national] J Math Sci , Springer

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Herz-type Sobolev spaces on domains

We introduce Herz-type Sobolev spaces on domains, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces. Some remarks on CaffarelliKohnNirenberg inequality are given.
Citation

M. DRIHEM Douadi, (2022), "Herz-type Sobolev spaces on domains", [national] Le Matematiche , Dipartimento di Matematica e Informatica Università di Catania, Viale A. Doria, n.6, 95125 Catania,, Italy

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On the composition operators on Besov and Triebel–Lizorkin spaces with power weights

Let G:R→R be a continuous function. Under some assumptions on G, s,α,p and q we prove that
{G(f):f∈Asp,q(Rn,|⋅|α)}⊂Asp,q(Rn,|⋅|α)
implies that G is a linear function. Here Asp,q(Rn,|⋅|α) stands either for the Besov space Bsp,q(Rn,|⋅|α) or for the Triebel–Lizorkin space Fsp,q(Rn,|⋅|α). These spaces unify and generalize many classical function spaces such as Sobolev spaces with power weights.
Citation

M. DRIHEM Douadi, (2022), "On the composition operators on Besov and Triebel–Lizorkin spaces with power weights", [national] Annales Polonici Mathematici , The Institute of Mathematics, Polish Academy of sciences

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Restricted Boundedness of Translation Operators on Variable Lebesgue Spaces

In this paper, we investigate the inequality

∥f(⋅+h)∥p(⋅)≤A∥f∥p(⋅),h∈Rn,A>0
under some suitable assumptions on the function f and the variable exponent p.
Citation

M. DRIHEM Douadi, (2022), "Restricted Boundedness of Translation Operators on Variable Lebesgue Spaces", [national] Current Trends in Analysis, its Applications and Computation , Springer

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Composition operators on Herz-type Triebel–Lizorkin spaces with application to semilinear parabolic equations

Let G:R→R
be a continuous function. In the first part of this paper, we investigate sufficient conditions on G such that

{G(f):f∈K˙αp,qFsβ}⊂K˙αp,qFsβ

holds. Here K˙αp,qFsβ are Herz-type Triebel–Lizorkin spaces. These spaces unify and generalize many classical function spaces such as Lebesgue spaces of power weights, Sobolev and Triebel–Lizorkin spaces of power weights. In the second part of this paper we will study local and global Cauchy problems for the semilinear parabolic equations

∂tu−Δu=G(u)

with initial data in Herz-type Triebel–Lizorkin spaces. Our results cover the results obtained with initial data in some known function spaces such us fractional Sobolev spaces. Some limit cases are given.
Citation

M. DRIHEM Douadi, (2022), "Composition operators on Herz-type Triebel–Lizorkin spaces with application to semilinear parabolic equations", [national] Banach Journal of Mathematical Analysis volume , Springer

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Semilinear parabolic equations in Herz spaces

In this paper, we will study local and global Cauchy problems for the semilinear parabolic equations ∂tu−Δu=G(u) with initial data in Herz spaces. These spaces unify and generalize many classical function spaces such as Lebesgue spaces of power weights. Our results cover the results obtained with initial data in Lebesgue spaces. Moreover, the results in Herz spaces are a little different from the results in Lebesgue spaces.
Citation

M. DRIHEM Douadi, (2022), "Semilinear parabolic equations in Herz spaces", [national] Applicable Analysis , Taylor & Francis

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2020

Variable Triebel-Lizorkin-type spaces

In this paper, we study Triebel–Lizorkin-type spaces with variable smoothness and integrability. We show that our space is well-defined, i.e., independent of the choice of basis functions and we obtain their atomic characterization. Moreover, the Sobolev embeddings for these function spaces are obtained.
Citation

M. DRIHEM Douadi, (2020), "Variable Triebel-Lizorkin-type spaces", [international] Bull. Malays. Math. Sci. Soc. , Springer

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2019

Real interpolation with variable exponent

We present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the case of fixed exponent. An application, we give the real interpolation of variable Besov and Lorentz spaces as introduced recently in Almeida and Hästö (J. Funct. Anal. 258 (5) 1628-2655, 2010) and L. Ephremidze et al. (Fract. Calc. Appl. Anal. 11 (4) (2008), 407-420).
Citation

M. DRIHEM Douadi, (2019), "Real interpolation with variable exponent", [national] Le Matematiche , Dipartimento di Matematica e Informatica Università di Catania, Viale A. Doria, n.6, 95125 Catania, Italy

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Jawerth-Franke embeddings of Herz-type Besov and Triebel-Lizorkin spaces,

In this paper we prove the Jawerth--Franke embeddings of Herz-type Besov and Triebel-Lizorkin spaces. Moreover, we obtain the Jawerth-Franke embeddings of Besov and Triebel-Lizorkin spaces equipped with power weights, and we prove the necessity of some assumptions on the parameters. As an application we present new embeddings between Besov and Herz spaces.
Citation

M. DRIHEM Douadi, (2019), "Jawerth-Franke embeddings of Herz-type Besov and Triebel-Lizorkin spaces,", [national] Funct. Approx. Comment. Math. , Project Euclid

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Variable Besov spaces. Continuous version,

We introduce Besov spaces with variable smoothness and integrability by using the continuous version of Calderón reproducing formula. We show that our space is well-defined, i.e., independent of the choice of basis functions. We characterize these function spaces by so-called Peetre maximal functions and we obtain the Sobolev embeddings for these function spaces. We use these results to prove the atomic decomposition for these spaces.
Citation

M. DRIHEM Douadi, (2019), "Variable Besov spaces. Continuous version,", [national] J. Math. Study, , GLOBAL SCIENCE PRESS

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On the duality of variable Triebel-Lizorkin spaces

The aim of this paper is to prove the duality of Triebel–Lizorkin spaces Fα(⋅)1,q(⋅). First, we prove the duality of associated sequence spaces. The result follows from the so-called φ-transform characterization in the sense of Frazier and Jawerth.
Citation

M. DRIHEM Douadi, (2019), "On the duality of variable Triebel-Lizorkin spaces", [national] Collectanea Mathematica , Springer

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Continuity of non regular pseudodifferential operators on variable Triebel-Lizorkin spaces.

This paper is concerned with the boundedness of nonregular pseudodifferential operators with symbols belonging to certain vector-valued Besov space, on Triebel–Lizorkin spaces with variable smoothness and integrability. These symbols include the classical Hörmander classes. Our results cover the results on Triebel–Lizorkin spaces with fixed exponents.
Citation

M. DRIHEM Douadi, Hebbache Wafa, , (2019), "Continuity of non regular pseudodifferential operators on variable Triebel-Lizorkin spaces.", [national] Annales Polonici Mathematici , The Institute of Mathematics, Polish Academy of sciences

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Complex interpolation of variable Triebel-Lizorkin spaces

We study complex interpolation of variable Triebel–Lizorkin spaces, especially we present the complex interpolation of and spaces. Also, some limiting cases are given.
Citation

M. DRIHEM Douadi, (2019), "Complex interpolation of variable Triebel-Lizorkin spaces", [national] Nonlinear Analysis, , sciencedirect

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On the continuity of pseudo-differential operators on multiplier spaces associated to Herz-type Triebel-Lizorkin spaces

In this paper, for a certain range of parameters, we prove that there exist symbols in the Hörmander class S01,0 which do not define bounded operators on M(K˙α,pqFsβ). To do these, we need the characterization of Herz–Besov spaces by ball means of differences and some properties of pointwise multipliers for Herz–Triebel–Lizorkin spaces.
Citation

M. DRIHEM Douadi, (2019), "On the continuity of pseudo-differential operators on multiplier spaces associated to Herz-type Triebel-Lizorkin spaces", [national] Mediterranean Journal of Mathematics , Springer

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Boundedness of some bilinear operators on variable Herz-type Hardy spaces

This paper is concerned with proving some estimate on variable Herz-type Hardy spaces of bilinear operators
B(f,g)(x)=∑γ=1N(T1γf)(x)(T2γg)(x),x∈Rn,
where N∈N , T1γ and T2γ are operators satisfying certain conditions. More precisely we prove the boundedness of B from HK˙α1(⋅),q1(⋅)p1(⋅)(Rn)×K˙α2(⋅),q2(⋅)p2(⋅)(Rn) into HK˙α(⋅),q(⋅)p(⋅)(Rn) and from HK˙α1(⋅),q1(⋅)p1(⋅)(Rn)×HK˙α2(⋅),q2(⋅)p2(⋅)(Rn) into HK˙α(⋅),q(⋅)p(⋅)(Rn) , with some appropriate assumptions on the parameters α(⋅) , αi(⋅) , p(⋅) , pi(⋅) , q(⋅) and qi(⋅) , i=1,2 . Our results cover the results on Herz-type Hardy spaces with fixed exponents.
Citation

M. DRIHEM Douadi, (2019), "Boundedness of some bilinear operators on variable Herz-type Hardy spaces", [national] Journal of Pseudo-Differential Operators and Applications , Springer

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Function spaces with general weights

We introduce Besov and Triebel-Lizorkin spaces with general smoothness. These spaces unify and generalize the classical Besov and Triebel-Lizorkin spaces.
We establish the phi-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. We study complex interpolation of these function spaces by using the Calderón product method and we identify their duals. We establish the smooth atomic, molecular and wavelet decomposition of these function spaces. To do these we need a generalization of some maximal inequality to the case of general weights.
Citation

M. DRIHEM Douadi, (2019), "Function spaces with general weights", [international] 12th ISAAC Congress , Portugal

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Spline representations of Triebel-Lizorkin spaces with general weights

In this paper we introduce some new Lizorkin–Triebel type spaces of variable smoothness. Here the smoothness lies in a new weighted class. We give some equivalent quasinorms and their characterizations via oscillations. We show that the box splines and tensor-products of B-splines are suitable to obtain the stable representations of functions of these spaces.
Citation

M. DRIHEM Douadi, (2019), "Spline representations of Triebel-Lizorkin spaces with general weights", [international] 30th International Workshop on Operator Theory and its Applications, IWOTA2O19 , Portugal

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2018

Complex interpolation of Herz-type Triebel-Lizorkin spaces

We study complex interpolation of Herz‐type Triebel–Lizorkin spaces by using the Calderón product method. Additionally we present complex interpolation between Herz‐type Triebel–Lizorkin spaces and Triebel–Lizorkin spaces F(infinity,s, beta). Moreover, we apply these results to obtain the complex interpolation of Triebel–Lizorkin spaces equipped with power weights and between bmo of hp spaces and Herz spaces.
Citation

M. DRIHEM Douadi, (2018), "Complex interpolation of Herz-type Triebel-Lizorkin spaces", [national] Math. Nachr , Wiley Online Library

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2017-01-01

Herz type Besov spaces of variable smoothness and integrability

In this paper, Herz-type Besov spaces with variable smoothness and integrability are introduced. Our scale contains variable Besov spaces as special cases. We prove several basic properties, especially the Sobolev-type embeddings.
Citation

M. DRIHEM Douadi, (2017-01-01), "Herz type Besov spaces of variable smoothness and integrability", [national] Kodai Math. J , Project Euclid

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2017

Sobolev Embeddings for Herz-Type Triebel-Lizorkin Spaces

In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin spaces, K˙α2,rqFs2θ↪K˙α1,psFs1β where the parameters α1,α2,s1,s2,s,q,r,p,β and θ satisfy some suitable conditions. An application we obtain new embeddings between Herz and Triebel-Lizorkin spaces. Moreover, we present the Sobolev embeddings for Triebel-Lizorkin spaces equipped with power weights. All these results cover the results on classical Triebel-Lizorkin spaces.
Citation

M. DRIHEM Douadi, (2017), "Sobolev Embeddings for Herz-Type Triebel-Lizorkin Spaces", [international] Function Spaces and Inequalities , New Delhi, India, December 2015

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Boundedness of non regular pseudodifferential operators on variable Besov spaces

We study the boundedness of non regular pseudodifferential operators, with symbols belonging to certain vector-valued Besov space, on Besov spaces with variable smoothness and integrabilty. These symbols include the classical Hörmander classes.
Citation

M. DRIHEM Douadi, Hebbache Wafa, , (2017), "Boundedness of non regular pseudodifferential operators on variable Besov spaces", [national] J. Pseudo-Differ. Oper. Appl , Springer

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2016

Notes on the Herz-type Hardy spaces of variable smoothness and integrability

The aim of this paper is twofold. First we give a new norm equivalents of the variable Herz spaces Kα(·)p(·),q(·) (Rn) and ˙Kα(·) p(·),q(·) (Rn) . Secondly we use these results to prove the atomic decomposition for Herz-type Hardy spaces of variable smoothness and integrability. Also, we prove the boundedness of a wide class of sublinear operators on these spaces, which includes maximal, potential and Calder´on-Zygmund operators
Citation

M. DRIHEM Douadi, (2016), "Notes on the Herz-type Hardy spaces of variable smoothness and integrability", [national] Mathematical Inequalities and Applications , Ele-Math

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Characterization of variable Besov-type spaces by ball means of differences

With the help of the maximal function characterizations of Besov-type spaces with variable smoothness and integrability we prove the characterization by ball means of differences for these function spaces.
Citation

M. DRIHEM Douadi, (2016), "Characterization of variable Besov-type spaces by ball means of differences", [national] Kyoto Journal of Mathematics , Project Euclid

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2015

Some characterizations of variable Besov-type spaces

The aim of this paper is to study properties of Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the φ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces.
Citation

M. DRIHEM Douadi, (2015), "Some characterizations of variable Besov-type spaces", [national] Annals of Functional Analysis , Project Euclid

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Some properties of variable Besov-type spaces

In this article we introduce Besov-type spaces with variable smoothness and integrability, which unify and generalize the Besov-type spaces with fixed exponents. Under natural regularity assumptions on the exponent functions, we show that our spaces are well-defined, i.e., independent of the choice of basis functions and we establish some properties of these function spaces. Moreover the Sobolev embeddings for these function spaces are obtained.
Citation

M. DRIHEM Douadi, (2015), "Some properties of variable Besov-type spaces", [national] Funct. Approx. Comment. Math. , Project Euclid

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2013

Atomic decomposition of Besov-type and Triebel-Lizorkin-type spaces

With the help of the maximal function caracterizations of the Besov-type space B p,qs,τ and the Triebel-Lizorkin-type space F p,qs,τ, we present the atomic decomposition of these function spaces. Our results cover the results on classical Besov and Triebel-Lizorkin spaces by taking τ = 0.
Citation

M. DRIHEM Douadi, (2013), "Atomic decomposition of Besov-type and Triebel-Lizorkin-type spaces", [national] Science China mathematics. , Springer

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Embeddings properties on Herz-type Besov and Triebel-Lizorkin spaces

We study the embeddings problems on Herz-type Besov-Triebel-Lizorkin spaces. In particular we will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Besov and Triebel-Lizorkin spaces.
Citation

M. DRIHEM Douadi, (2013), "Embeddings properties on Herz-type Besov and Triebel-Lizorkin spaces", [national] Mathematical Inequalities and Applications. , Ele-Math's journals

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2012

Maximal, potential and singular type operators on Herz spaces with variable exponents

We investigate both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents. Under natural regularity assumptions on the exponent functions, we prove the boundedness of a wide class of sublinear operators on these spaces, which includes maximal, potential and Calderón–Zygmund operators.
Citation

M. DRIHEM Douadi, Alexandre Almeida, , (2012), "Maximal, potential and singular type operators on Herz spaces with variable exponents", [national] Journal of Mathematical Analysis and Applications. , science direct

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Atomic decomposition of Besov spaces of variables smoothness and integrability

The aim of this paper is twofold. First we characterize the Besov spaces with variable smoothness and integrability by so-called Peetre maximal functions. Secondly we use these results to prove the atomic decomposition for these spaces.
Citation

M. DRIHEM Douadi, (2012), "Atomic decomposition of Besov spaces of variables smoothness and integrability", [national] Journal of Mathematical Analysis and Applications , science direct

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Characterizations of Besov-type and Triebel-Lizorkin-type spaces by differences.

We present characterizations of the Besov-type spaces ?(?,??,?) and the Triebel-Lizorkin-type spaces ?(?,??,?) by differences. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking ?=0.
Citation

M. DRIHEM Douadi, (2012), "Characterizations of Besov-type and Triebel-Lizorkin-type spaces by differences.", [international] Journal of function spaces and applications. , Hindawi , USA

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2011

Some characterizations of function spaces connecting L(lamda,2) spaces

In this paper, with the help of the equivalent norms based on maximal functions, we present characterization of the B(s,τ,p,q )spaces by means of differences.
Citation

M. DRIHEM Douadi, (2011), "Some characterizations of function spaces connecting L(lamda,2) spaces", [national] Rev. Mat. Complut. , Springer

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2009

Some embeddings and equivalent norms of the L(lamda,p,q) spaces

The aim of this paper is to give some properties for the L(λ,s,p,q )spaces, especially concerning embeddings and equivalent norms based of maximal functions and local means.
Citation

M. DRIHEM Douadi, (2009), "Some embeddings and equivalent norms of the L(lamda,p,q) spaces", [national] Functiones et approximation , Project Euclid

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2006

Boundedness of Some Pseudodifferential Operators on Bessel-Sobolev Space

We study the continuity of generalized pseudodi erential operator B ; on Sobolev- Bessel space, with > 􀀀1=2 and  in the class of symbols. Also, we give the analogous result related to the commutator [B ; ; I' ] where I' = F􀀀1B ('FB ()) and ' is being a suitable function.
Citation

M. DRIHEM Douadi, (2006), "Boundedness of Some Pseudodifferential Operators on Bessel-Sobolev Space", [national] Mathematica Balkanica , The National Committee for Mathematics of Bulgaria and the Bulgarian Academy of Sciences

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On the pointwise multiplication in Besov and Lizorkin-Triebel spaces

Under some sufficient conditions satisfied by F-space of Lizorkin and Triebel and B-space of Besov, we prove some embeddings of types F⋅B↪F, F⋅F↪F, and B⋅B↪B.
Citation

M. DRIHEM Douadi, (2006), "On the pointwise multiplication in Besov and Lizorkin-Triebel spaces", [national] International Journal of Mathematics and Mathematical Sciences , Hindawi

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2002-01-01

Some embeddings into the multiplier spaces associated to Besov and Lizorkin-Triebel spaces

We study the set of pointwise multipliers in the Lizorkin-Triebel space F(s,p,q) and of the corresponding multiplier set in the Besov space B(s,p,q) , where we give sufficient conditions on the parameters s,p and p1 such that the embeddings L(infinity) ↪ M(F(s,p,q)) and B(n/p1,p1,infinity)↪ M(B(s,p,q)) hold.
Citation

M. DRIHEM Douadi, (2002-01-01), "Some embeddings into the multiplier spaces associated to Besov and Lizorkin-Triebel spaces", [national] Z. Anal. Anwendungen , EMS PRESS

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