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
Feuto, Justin 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
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Feuto, Justin. 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. http://archive.numdam.org/articles/10.5802/ambp.340/

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

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

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

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

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

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

[7] Dosso, M.; Fofana, I.; Sanogo, M. 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] Fan, D.; LU, S.; Yang, D. 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] Feichtinger, H. G. A characterization of Wiener’s algebra on locally compact groups, Arch. Math. (Basel), Volume 29 (1977), pp. 136-140 | DOI | MR | Zbl

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

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

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

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

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

[16] Gogatishvili, A.; Mustafayev, R. 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] Grafakos, L. Modern Fourier analysis, 250, Springer, New York, second edition, 2009 | MR | Zbl

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

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

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

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