Norm inequalities in some subspaces of Morrey space
Annales mathématiques Blaise Pascal, Volume 21 (2014) no. 2, pp. 21-37.

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

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

DOI: 10.5802/ambp.340
Classification: 42B35,  42B20,  42B25
Keywords: Amalgams spaces, fractional maximal operator, Riesz potential, Hilbert transform
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
DA  - 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/
UR  - https://www.ams.org/mathscinet-getitem?mr=3322613
UR  - https://doi.org/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://doi.org/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, Volume 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 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

Cited by Sources: