M. DJERIOU Aissa

Prof

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Department

Mathematics Department

Research Interests

Analyse fonctionnelle, Continuité des opérateurs pseudo-différentiels, Equations aux dérivées partielles, Théorie des Opérateurs. Analyse fonctionnelle, Continuité des opérateurs pseudo-différentiels, Équations aux dérivées partielles, Théorie des Opérateurs.

Contact Info

University of M'Sila, Algeria

Email : aissa.djeriou@univ-msila.dz

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Recent Publications

2025-12-20

Strongly Singular Convolution Operators and their Commutators on Variable Herz-type Hardy Spaces

The aim of this paper is to prove that strongly singular convolution operators are bounded from $H\dot{K}_{{p(\cdot )}}^{{\alpha (\cdot )},q{(\cdot )}}(\mathbb{R}^{n})$ to $\dot{K}_{{p(\cdot )}}^{{\alpha (\cdot)},q{(\cdot )}}(\mathbb{R}^{n})$ when $\alpha \left( 0\right) =n-n/p\left(0\right) $ and $\alpha _{\infty }=n-n/p_{\infty }$. Also, the boundedness of their commutators from the inhomogeneous Herz-type Hardy spaces to the inhomogeneous Herz spaces has been obtained.
Citation

M. DJERIOU Aissa, rabah.heraiz@univ-msila.dz, , (2025-12-20), "Strongly Singular Convolution Operators and their Commutators on Variable Herz-type Hardy Spaces", [national] Khayyam Journal of Mathematics (KJM) , Department of Mathematics at Ferdowsi University of Mashhad

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2024-12-13

Boundedness of some bilinear operators on variable Morrey spaces

In this paper, the author obtains the boundedness of certain bilinear operators that can be formally
written in the integral form of
| ( , )( )|≤ | (
) ( + )|
| |
for all
such that 0
( (
. )
,
∈ ,
( ( + .) on variable Morrey spaces.
Furthermore, the similar definitions and results of multilinear operators are obtained.
Citation

M. DJERIOU Aissa, (2024-12-13), "Boundedness of some bilinear operators on variable Morrey spaces", [international] The 5th International Conference on Mathematical, Engineering and Management Sciences. , India.

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2024-12-07

Boundedness of commutator of fractional maximal operator on Lorentz-Herz spaces

In this work, the author obtain the boundedness of the fractional maximal commutators Ma and the
commutators of the fractional maximal operator [aM] in the homogeneous Lorentz-Herz spaces K q
where M, Ma and [aM] are respectively de ned by
Mf(x) =sup
r>0
Ma f(x) = sup
B(xr) 1+
B(xr) 1+
n
n
B(xr)
f(y)dy 0 <n
a(x) a(y) f(y)dy a L1
loc(Rn)
r>0
and
B(xr)
[aM](f)(x) = a(x)M(f)(x) M(af)(x)
ps (Rn),
The Lorentz-Herz space is a generalization of the generalized Lorentz spaces and the Herz spaces. My results
generalize and extend the corresponding results of Guliyev and Ho (see [3, 6]).
Citation

M. DJERIOU Aissa, (2024-12-07), "Boundedness of commutator of fractional maximal operator on Lorentz-Herz spaces", [national] The 4th National Conference of Mathematics and Applications "CNMA - 2024" , Université de Mila

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2024-11-28

Boundedness of some sublinear operators on mixed Herz spaces

In this paper, mixed Herz spaces are introduced, and its block decomposition theory is established. Also, the authors study the boundedness of some sublinear operators on these spaces by using the block decomposition. Our results generalize and extend the corresponding results of Lu and Yang [ Acta Math. Sinica (New Ser.). 13 (1997)].
Citation

M. DJERIOU Aissa, Rabah.Heraiz@univ-msila.dz, , (2024-11-28), "Boundedness of some sublinear operators on mixed Herz spaces", [national] Journal of Applied Mathematics and Informatics , Korean Society for Computational and Applied Mathematics

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2024-06-30

Anisotropic Variable Herz Spaces and Applications

In this study, we establish some new characterizations for a class of anisotropic Herz spaces in which all exponents are considered as variables. We also provide a description of these spaces based on bloc decomposition. As an application, we investigate the boundedness of certain sublinear operators within these function spaces.
Citation

M. DJERIOU Aissa, Rabah.Heraiz@univ-msila.dz, , (2024-06-30), "Anisotropic Variable Herz Spaces and Applications", [national] Kyungpook Mathematical Journal , Department of Mathematics, Kyungpook National University

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2024-06-04

TP de langage Latex

TEX est un logiciel d’édition développé par Donald KNUTH, puis modifié par Leslie LAMPORT (LATEX) permettant de produire des documents de qualité digne de la publication professionnelle.
Citation

M. DJERIOU Aissa, (2024-06-04), "TP de langage Latex", [national]

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2024-03-17

Cours d'algèbre multilinéaire

Ce polycopi ́e est le fruit des ann ́ees d’enseignement de modules d’Alg`ebre multilin ́eaire pour
la premi`ere ann ́ee master Analyse fonctionel domain math ́ematique et Informatique fili`ere
math ́ematique.
Chaque chapitre est subdivis ́e en rappel complet, un cours et des exemples, suivis par
une s ́erie d’exercices avec des solutions detai ́ee. Le but de ce polycopi ́e est de donn ́ee des
initiations de l’Alg`ebre lin ́eaire et de l’Alg`ebre multilin ́eaire.
Au d ́ebut, je parlerai de la structure d’espaces et sous-espaces vectoriels qui sont des
structures alg ́ebriques que l’on retrouve quasiment partout en math ́ematiques et qui sont
la structure de base en alg`ebre lin ́eaire. La notion d’espace vectoriel est une structure
fondamentale en math ́ematiques modernes.
Dans le deuxi`eme chapitre, on aborde la notion des applications multilin ́eaires et les
formes bilin ́eaires et les formes quadratiques (d ́efinition, et toutes leurs propri ́et ́es).
Dans le troisi`eme chapitre nous rappelons les in ́egalit ́es de Cauchy-Schwarz et Minkowski,
la notion d’orthogonalisation, les bases orthogonale, la m ́ethode d’orthogonalisation de
Gram-Schmid et les d ́efinitions et propri ́et ́es de produit scalaire.
Dans le quatrei`eme chapitre on rappelons les notions pr ́eliminaire de formes sesquilin ́eaires
hermitiennes, formes quadratiques, et le produit scalaire hermitien ; Leurs d ́efinitions et propri ́et ́es. A la fin du chapitre on expose la notion d’espace hermitien, et les endomorphismes
d’un espace hermitien, en particulier les endomorphismes adjoints, les endomorphismes unitaires, les endomorphismes normaux, et les endomorphismes hermitiens.
Enfin, j’esp`ere que l’ ́etudiant et l’enseignant des math ́ematiques trouvent leurs besoins
dans ce polycopi ́e
Citation

M. DJERIOU Aissa, (2024-03-17), "Cours d'algèbre multilinéaire", [national] Université de M'sila

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2024-01-20

Localization property of generalized Besov-type spaces, Triebel-Lizorkin-type spaces and their associated multiplier spaces

In this paper, we study the localization property of generalized Besov-type spaces, Triebel-
Lizorkin-type spaces and their associated multiplier spaces, defined from function v : [0, ∞) →]0, ∞)
satisfying the inequality v(ts) ≥ c t−μv(s) for 0 < t, s ≤ 1 and some real μ.
Citation

M. DJERIOU Aissa, (2024-01-20), "Localization property of generalized Besov-type spaces, Triebel-Lizorkin-type spaces and their associated multiplier spaces", [national] Filomat , Faculty of Sciences and Mathematics, University of Niˇs, Serbia

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2023-11-06

On Mixed Herz Spaces and Applications

In this paper, mixed Herz spaces are introduced, and its block decomposition theory is established. Also, the
authors study the boundedness of some sublinear operators on these spaces by using the block decomposition.
Our results generalize and extend the corresponding results of Lu and Yang [ Acta Math. Sinica (New Ser.). 13
(1997)]
Citation

M. DJERIOU Aissa, (2023-11-06), "On Mixed Herz Spaces and Applications", [international] The first Sharjah International Conference on Mathematical Sciences , University of Sharjah, 6th-8th November 2023

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2022

THE ATOMIC DECOMPOSITION OF HERZ-MORREY TYPE HARDY SPACES WITH MIXED NORM AND ITS APPLICATION

In this communication, mixed Herz-Morrey-Hardy space is presented and its atom-decomposition theory is established. This result generalizes and extends the corresponding results of XU and Yang. Also, the author studies the boundedness of fractional integral operators on mixed Herz-Morrey-Hardy spaces by using atomic decomposition.
Citation

M. DJERIOU Aissa, (2022), "THE ATOMIC DECOMPOSITION OF HERZ-MORREY TYPE HARDY SPACES WITH MIXED NORM AND ITS APPLICATION", [international] International conference in Operator theory,PDEand Applications , Echahid Hamma Lakhdar University–El Oued

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Some pseudo-differential Operators on generalized Herz-type Triebel-Lizorkin Spaces

In this work, we study the continuity of pseudo-differential operators on
Herz-type Triebel-Lizorkin spaces $K_{q}^{\alpha ,p}F_{\beta }^{v_{\mu
}}\left( \mathbb{R}^{n}\right) $, under some parameters $\beta ,p,q$, $%
\alpha $ and $v:\ \left[ 0,\infty \right) \rightarrow ]0,\infty )$ be a
function such that the inequality $v(ts)\geq c\,t^{-\mu }v(s)$ holds for $%
0<t,s\leq 1$ and some real $\mu $.
Citation

M. DJERIOU Aissa, (2022), "Some pseudo-differential Operators on generalized Herz-type Triebel-Lizorkin Spaces", [national] Conférence Nationale de Mathématiques et Applications , Université de Mila

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Sobolev type embeddings for variable Herz-Morrey-type Besov spaces

In this communication, I will present some results concerning Herz-Morrey-type Besov
spaces with variable smoothness and integrability, which covers Herz-Morrey-type Besov
spaces with fixed exponents, these spaces were first introduced by B. Dong and J. Xu
Citation

M. DJERIOU Aissa, (2022), "Sobolev type embeddings for variable Herz-Morrey-type Besov spaces", [international] International Workshop on Applied Mathematics and Modelling , Université 8 Mai 1945 Guelma

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2021

Some results concerning localization property of generalized Herz, Herz-type Besov spaces and Herz-type Triebel-Lizorkin spaces

Y. Komori and K. Matsuoka in 2009, we define Herz-type Besov spaces and Herz-type Triebel-Lizorkin spaces , which cover the Besov spaces and the Triebel-Lizorkin spaces in the homogeneous case, where is a sequence of non-negative numbers such that\begin {equation*} C^{-1} 2^{\delta (kj)}\leq\frac {\theta (k)}{\theta (j)}\leq C2^{\alpha (kj)},\quad k> j,\end {equation*} for some ( and are numbers in ). Further, under the condition mentioned above on , we prove that and are localizable in the -norm for , and is localizable in the -norm, ie there exists satisfying , for any , such that\begin {equation*}\left\Vert f| E\right\Vert\approx\Big (\underset {k\in\mathbb {Z}^{n}}{\sum}\left\Vert\varphi (\cdot-k)\cdot f| E\right\Vert^{q}\Big)^{1/q}.\end {equation*} Results presented in this paper improve and generalize some known corresponding results in some function spaces
Citation

M. DJERIOU Aissa, (2021), "Some results concerning localization property of generalized Herz, Herz-type Besov spaces and Herz-type Triebel-Lizorkin spaces", [national] Carpathian Mathematical Publications , Carpathian Mathematical Publications

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CONTINUITY OF PSEUDO-DIFFERENTIAL OPERATORS ON LOCALIZED BESOV-TYPE SPACES

We will study the continuity of some pseudo-differential operators on the localized Besov–type spaces, under some conditions on s and t.
Citation

M. DJERIOU Aissa, (2021), "CONTINUITY OF PSEUDO-DIFFERENTIAL OPERATORS ON LOCALIZED BESOV-TYPE SPACES", [international] International Conference on Pure and Applied Mathematics , Ouargla University

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Some results on anisotropic variable Herz spaces

In this paper, mixed Herz-type Hardy space is introduced and its atom decomposition
theory is established. This result generalizes and extends the corresponding
results of Lu and Yang in classical spaces. Also, the authors study the boundedness
of fractional integral operators on mixed Herz-type Hardy spaces by using atomic
decomposition.
Citation

M. DJERIOU Aissa, (2021), "Some results on anisotropic variable Herz spaces", [national] PREMIÈRE CONFÉRENCE NATIONALE DES MATHÉMATIQUES PURES ET APPLIQUÉES EN LIGNE , Université Larbi Tebessi– Tebessa

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2019

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. DJERIOU Aissa, (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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2018

Localization property of generalized Besov-type spaces

We study the localization property of generalized Besov-type spaces, defined from function v: [0,∞)→]0,∞) satisfying the inequality v(ts)≥ct^{-μ}v(s) for 0<t,s≤1 and some real μ.
Citation

M. DJERIOU Aissa, (2018), "Localization property of generalized Besov-type spaces", [national] 5 ème Journée de Mathématiques , M'sila

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2017

Cours d'algèbre 1

Cours d'algèbre 1
Citation

M. DJERIOU Aissa, (2017), "Cours d'algèbre 1", [national] Msila

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Continuity of pseudo-differential operators on localized Besov-type spaces

We will study the continuity of some pseudo-differential operators on the localized Besov--type spaces (B_{p,q}^{s,τ}(Rⁿ))_{ℓ^{r}}, under some conditions on s and τ.
Citation

M. DJERIOU Aissa, (2017), "Continuity of pseudo-differential operators on localized Besov-type spaces", [national] 4 ème Journée de Mathématiques , M'sila

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2016

Cours d'algèbre 2

Cours d'algèbre 2
Citation

M. DJERIOU Aissa, (2016), "Cours d'algèbre 2", [national] Msila

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La Continuité des opérateurs pseudo-différentiels sur les espaces des Triebel-Lizorkin généralisé localisé

Nous étudions la continuité des opérateurs pseudo-différentiels d'ordre m, avec un symbole σ(x,ξ), qui appartiennent à la classe de Hörmander S_{1,δ}^{m} où 0≤δ<1, sur les espaces de Triebel-Lizorkin généralisé localisé (F_{p,q}^{v_{μ}})_{ℓ^{r}}. Ces espaces sont définis par une fonction positive v_{μ}:[0,∞)→]0,∞) qui vérifie

sup_{0<t<1}t^{-μ}sup_{0<s≤1}((v_{μ}(s))/(v_{μ}(ts)))<+∞.
Citation

M. DJERIOU Aissa, (2016), "La Continuité des opérateurs pseudo-différentiels sur les espaces des Triebel-Lizorkin généralisé localisé", [national] 3 ème Journée de Mathématiques , M'sila

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2015

Some pseudo-differential operators on Morrey-Besov spaces

Some pseudo-differential operators on Morrey-Besov spaces
Citation

M. DJERIOU Aissa, (2015), "Some pseudo-differential operators on Morrey-Besov spaces", [national] 2 ème Journée de Mathématiques , M'sila

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2014

Composition operator in Morrey spaces

Composition operator in Morrey spaces
Citation

M. DJERIOU Aissa, (2014), "Composition operator in Morrey spaces", [national] 1 ere Journée de Mathématiques , M'sila

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Atomic decomposition for Herz spaces.

Atomic decomposition for Herz spaces.
Citation

M. DJERIOU Aissa, (2014), "Atomic decomposition for Herz spaces.", [international] 4éme Workshop Internationel sur les mathématiques Appliquées et la Modélisation, WIMAM'2014 , Guelma

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2013

Pseudodifferential Operators on Herz type Besov space

In this work, we will be interested by the Herz-type Besov spaces H_{q}^{α,p}B_{β}^{s}(Rⁿ), this new class of function spaces is defined as the set of all tempered distributions f, such that
‖f‖_{K_{q}^{α,p}B_{β}^{s}}=(∑_{j=0}(2^{sj}‖F⁻¹(φ_{j}Ff)‖_{K_{q}^{α,p}})^{β})^{1/β}<+∞,
where s∈R, 0<β,p,q≤∞ and α>-n/q.
We will study on K_{q}^{α,p}B_{β}^{s}(Rⁿ) the boundedness of some pseudo-differential operators (ps.d.o.) σ(x,D) which is defined by the formula
σ(x,D)f(x)=(2π)⁻ⁿ∫_{Rⁿ}e^{ix⋅ξ}σ(x,ξ)f(ξ)dξ, (f∈S, x∈R),
where σ is a complex-valued and sufficiently differentiable function defined on Rⁿ×Rⁿ.
Citation

M. DJERIOU Aissa, (2013), "Pseudodifferential Operators on Herz type Besov space", [international] The 2nd Abu Dhabi university annual international conference : mathematical science and its applications , Abu Dhabi , UAE.

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2012

Boundedness of some pseudo-differential operators and commutator on Triebel-Lizorkin spaces

Boundedness of some pseudo-differential operators and commutator on Triebel-Lizorkin spaces
Citation

M. DJERIOU Aissa, (2012), "Boundedness of some pseudo-differential operators and commutator on Triebel-Lizorkin spaces", [national] Colloque national sur les sciences mathématiques, CNSM'10 , Tébbesa, Algérie.

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Boundedness of some pseudo-differential operators on generalized Besov-type spaces

We will study the boundedness of some pseudo-differential operators on the generalized Besov--Type spaces B_{p,q}^{v,τ}(Rⁿ), under some conditions on the positive function v: [0,∞)→R.
Citation

M. DJERIOU Aissa, (2012), "Boundedness of some pseudo-differential operators on generalized Besov-type spaces", [international] International Conference on Applied and Computational Mathematics, ICACM , Middle East technical university Ankara, Turkey.

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2011

On the pointwise multiplication of generalized Besov and Triebel-Lizorkin spaces

In the multiplication and mixed multiplication of generalized Lizorkin-Triebel space and generalized Besov space, this paper is concerned with proving some embeddings of the form

F⋅B↪F, F⋅F↪F and B⋅B↪B

where F and B, with three indices, will be defined the space of generalized Triebel-Lizorkin and the space of generalized Besov respectively. The different embeddings obtained here are under some conditions used by J. Franke [1986], J. Johnsen [1995] and J. Marschall [1994,1995].
Citation

M. DJERIOU Aissa, (2011), "On the pointwise multiplication of generalized Besov and Triebel-Lizorkin spaces", [international] 1er Workshop International sur les Mathématiques appliquées et la modélisation, WIMAM'2011. , Guelma, Algérie

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2010

Boundedness of some pseudo-differential operators on generalized localized Triebel-Lizorkin spaces

Boundedness of some pseudo-differential operators on generalized localized Triebel-Lizorkin spaces
Citation

M. DJERIOU Aissa, (2010), "Boundedness of some pseudo-differential operators on generalized localized Triebel-Lizorkin spaces", [international] Colloque International sur les Mathématiques appliquées, CIMA'10. , Guelma

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2009

A counterexample for boundedness of some pseudo-differential operators on pointwise multipliers Triebel-Lizorkin space

A counterexample for boundedness of some pseudo-differential operators on pointwise multipliers
Citation

M. DJERIOU Aissa, (2009), "A counterexample for boundedness of some pseudo-differential operators on pointwise multipliers Triebel-Lizorkin space", [national] Mathematica Balkanica , Mathematica Balkanica

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2008

School and Workshop on Dynamical Systems, International Centre for Theoretical Physics

School and Workshop on Dynamical Systems, International Centre for Theoretical Physics
Citation

M. DJERIOU Aissa, (2008), "School and Workshop on Dynamical Systems, International Centre for Theoretical Physics", [international] School and Workshop on Dynamical Systems, International Centre for Theoretical Physics , Trieste, Italy.

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2007

Continuity of certain pseudo-differentials operators on multipliers generalized Triebel-Lizorkin spaces

We treat the boundedness of some pseudo-differential operators of order 0 on pointwise multipliers Lizorkin-Triebel space M(F_{p,q}^{v_{a}} (Rⁿ)) where 1<p<∞, 1<q≤∞ and 0<a<n/p.
Citation

M. DJERIOU Aissa, (2007), "Continuity of certain pseudo-differentials operators on multipliers generalized Triebel-Lizorkin spaces", [international] The Second International Conference on Mathematics: Trends and Developments, ICMTD07. , Cairo, Egypt

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Continuity of pseudo-differentials operators on Companato spaces

Continuity of pseudo-differentials operators on Companato spaces
Citation

M. DJERIOU Aissa, (2007), "Continuity of pseudo-differentials operators on Companato spaces", [international] Colloque International sur les equation aux dérivées partielles et leurs applications , Guelma

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2006

Continuite des operateurs pseudo-differentiels sur les espaces de Lizorkin-Tribel généralisés

Continuite des operateurs pseudo-differentiels sur les espaces de Lizorkin-Tribel généralisés
Citation

M. DJERIOU Aissa, (2006), "Continuite des operateurs pseudo-differentiels sur les espaces de Lizorkin-Tribel généralisés", [international] 14ème Colloque de la Société Mathématiques de Tunisie , Tunisie

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Continuite des operateurs pseudo-differentiels sur les espaces de Besov définies par la transformtion de Fourier-Bessel

Continuite des operateurs pseudo-differentiels sur les espaces de Besov définies par la transformtion de Fourier-Bessel
Citation

M. DJERIOU Aissa, (2006), "Continuite des operateurs pseudo-differentiels sur les espaces de Besov définies par la transformtion de Fourier-Bessel", [international] RAMA5 , M'sila

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