Annales Mathématiques
Blaise Pascal
no. 2
Norm inequalities in some subspaces of Morrey space
[Inégalités en norme dans certains sous-espaces d’espaces de Morrey]
Justin Feuto1
1 Laboratoire de Mathématiques Fondamentales UFR Mathématiques et Informatique Université Félix Houphouët-Boigny Abidjan, Cocody 22 B.P 1194 Abidjan 22 Côte d’Ivoire
Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 2, pp. 21-37.

Nous établissons des inégalités en norme pour certains opérateurs classiques dans les amalgames et certains sous-espaces d’espaces de Morrey.

We give norm inequalities for some classical operators in amalgam spaces and in some subspaces of Morrey space.

DOI : 10.5802/ambp.340
Classification : 42B35, 42B20, 42B25
Keywords: Amalgams spaces, fractional maximal operator, Riesz potential, Hilbert transform
Mot clés : Espace amalgame, operateur maximal fractionnaire, potentiel de Riesz, transformation de Hilbert

Justin Feuto 1

1 Laboratoire de Mathématiques Fondamentales UFR Mathématiques et Informatique Université Félix Houphouët-Boigny Abidjan, Cocody 22 B.P 1194 Abidjan 22 Côte d’Ivoire 
@article{AMBP_2014__21_2_21_0,
     author = {Justin Feuto},
     title = {Norm inequalities in some subspaces  of {Morrey} space},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {21--37},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {21},
     number = {2},
     year = {2014},
     doi = {10.5802/ambp.340},
     mrnumber = {3322613},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.340/}
}
TY  - JOUR
AU  - Justin Feuto
TI  - Norm inequalities in some subspaces  of Morrey space
JO  - Annales mathématiques Blaise Pascal
PY  - 2014
SP  - 21
EP  - 37
VL  - 21
IS  - 2
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.340/
DO  - 10.5802/ambp.340
LA  - en
ID  - AMBP_2014__21_2_21_0
ER  - 
%0 Journal Article
%A Justin Feuto
%T Norm inequalities in some subspaces  of Morrey space
%J Annales mathématiques Blaise Pascal
%D 2014
%P 21-37
%V 21
%N 2
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.340/
%R 10.5802/ambp.340
%G en
%F AMBP_2014__21_2_21_0
Justin Feuto. Norm inequalities in some subspaces  of Morrey space. Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 2, pp. 21-37. doi : 10.5802/ambp.340. https://ambp.centre-mersenne.org/articles/10.5802/ambp.340/

[1] D.R. Adams A note on Riesz potentials, Duke Math. J., Volume 42 (1975), p. 765-778. | DOI | MR | Zbl

[2] D.R. Adams; J Xiao Nonlinear potential analysis on Morrey spaces and their capacities, Indiana University Mathematics Journal, Volume 53 (2004), p. 1629-1663. | DOI | MR | Zbl

[3] R. C. Busby; H. A. Smith Product-convolution operators and mixed-norm spaces, Trans. AMS, Volume 263 (1981), p. 309-341. | DOI | MR | Zbl

[4] F. Chiarenza; M. Frasca Morrey spaces and Hardy-Littlewood maximal function, Rend. Math., Volume 7 (1987), p. 273-279. | MR | Zbl

[5] M. Cowling; S. Meda; R. Pasquale Riesz potentials and amalgams, Ann. Inst. Fourier, Grenoble, Volume 49 (1999), pp. 1345-1367 | DOI | Numdam | MR | Zbl

[6] T. Dobler Wiener amalgam spaces on locally compact groups (1989) (Masters Thesis, University of Vienna)

[7] M. Dosso; I. Fofana; M. Sanogo On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals, Ann. Pol. Math., Volume 108 (2013), pp. 133-153 | DOI | MR | Zbl

[8] D. Fan; S. LU; D. Yang Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients, Georgian Math. J., Volume 5 (1998), p. 425-440. | DOI | MR | Zbl

[9] H. G. Feichtinger A characterization of Wiener’s algebra on locally compact groups, Arch. Math. (Basel), Volume 29 (1977), pp. 136-140 | DOI | MR | Zbl

[10] H. G. Feichtinger Banach convolution algebras of Wiener’s type, Functions, Series, Operators, Proc. Conf. Budapest, 38, Colloq. Math. Soc. János Bolyai (1980), pp. 509-524 | MR | Zbl

[11] J. Feuto; I. Fofana; K. Koua Espaces de fonctions á moyenne fractionnaire intgrables sur les groupes localement compacts, Afr. Mat., Volume 15 (2003), pp. 73-91 | MR | Zbl

[12] J. Feuto; I. Fofana; K. Koua Integrable fractional mean functions on spaces of homogeneous type, Afr. Diaspora J. Math., Volume 9 (2010), pp. 8-30 | MR | Zbl

[13] I. Fofana Étude d’une classe d’espaces de fonctions contenant les espaces de Lorentz, Afr. Mat., Volume 1 (1988), pp. 29-50 | MR | Zbl

[14] J. J. F. Fournier; J. Stewart Amalgams of l p and l q , Bull. Amer. Math. Soc, Volume 13 (1985), pp. 1-21 | DOI | MR | Zbl

[15] J. Garciá-Cuerva; J.L. Rubio de Francia Weighted norm inequalities and related topics, 116, North-Holland Math. Stud., 1985 | MR | Zbl

[16] A. Gogatishvili; R. Mustafayev Equivalence of norms of Riesz potential and fractional maximal function in Morrey-type spaces, Preprint, Institute of Mathematics, AS CR, Prague. (2008), pp. 7-14 | MR

[17] L. Grafakos Modern Fourier analysis, 250, Springer, New York, second edition, 2009 | MR | Zbl

[18] F. Holland Harmonic analysis on amalgams of l p and ℓ q , J. London Math. Soc., Volume 10 (1975), pp. 295-305 | DOI | MR | Zbl

[19] B. Muckenhoupt; R. Wheeden Weighted Norm Inequalities for Fractional Integrals, Trans. of the AMS, Volume 192 (1974), pp. 261-274 | DOI | MR | Zbl

[20] W. P. Ziemer Weakly differentiable functions, Springer-Verlag, 1989 | MR | Zbl

Cité par Sources :