Rough fractional integrals and its commutators on variable Morrey spaces

Tan, Jian; Zhao, Jiman

doi:10.1016/j.crma.2015.09.024

Harmonic analysis

Rough fractional integrals and its commutators on variable Morrey spaces
[Intégrales fractionnaires rugueuses et ses commutateurs sur les espaces de Morrey avec exposant variable]

Présenté par : the Editorial Board

Tan, Jian ¹ ; Zhao, Jiman ¹

¹ School of Mathematical Sciences, Beijing Normal University, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China

Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1117-1122.

Résumé
Abstract

Dans cet article, les auteurs obtiennent la bornitude des intégrales fractionnaires avec un noyau singulier dans des espaces de Morrey (avec exposant variable). De plus, la bornitude des commutateurs généralisés entre ces opérateurs et la multiplication par une fonction BMO est aussi considérée.

In this paper, the authors obtain the boundedness of fractional integrals with rough kernel on variable Morrey spaces. The corresponding boundedness for commutators generalized by the fractional integral and BMO function is also considered.

Reçu le : 2015-06-02
Accepté le : 2015-09-28
Publié le : 2015-11-02

DOI : 10.1016/j.crma.2015.09.024

Affiliations des auteurs :

Tan, Jian ¹ ; Zhao, Jiman ¹

¹ School of Mathematical Sciences, Beijing Normal University, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China

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     title = {Rough fractional integrals and its commutators on variable {Morrey} spaces},
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Tan, Jian; Zhao, Jiman. Rough fractional integrals and its commutators on variable Morrey spaces. Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1117-1122. doi : 10.1016/j.crma.2015.09.024. http://www.numdam.org/articles/10.1016/j.crma.2015.09.024/

Bibliographie
Cité par

[1] Capone, C.; Cruz-Uribe, D.; Fiorenza, A. The fractional maximal operators and fractional integrals on variable $L^{p}$ spaces, Rev. Mat. Iberoam., Volume 23 (2007), pp. 743-770

[2] Cruz-Uribe, D.; Fiorenza, A. Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Birkhäuser, Basel, Switzerland, 2013

[3] Cruz-Uribe, D.; Fiorenza, A.; Martell, J.; Pérez, C. The boundedness of classical operators on variable $L^{p}$ spaces, Ann. Acad. Sci. Fenn., Math., Volume 31 (2006), pp. 239-264

[4] Cruz-Uribe, D.; Wang, L. Variable Hardy spaces, Indiana Univ. Math. J., Volume 63 (2014) no. 2, pp. 447-493

[5] Diening, L.; Harjulehto, P.; Hästö, P.; Růz̆ička, M. Lebesgue and Sobolev Spaces with Variable Exponents, Springer, Heidelberg, Germany, 2011

[6] Hardy, G.; Littlewood, J. Some properties of fractional integrals, Math. Z., Volume 27 (1928), pp. 565-606

[7] Ho, K. Atomic decomposition of Hardy spaces and characterization of BMO via Banach function spaces, Anal. Math., Volume 38 (2012) no. 3, pp. 173-185

[8] Ho, K. The fractional integral operators on Morrey spaces with variable exponent on unbounded domains, Math. Inequal. Appl., Volume 16 (2013), pp. 363-373

[9] Izuki, M. Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent, Rend. Circ. Mat. Palermo, Volume 59 (2010), pp. 461-472

[10] Kováčik, O.; Rákosník, J. On spaces $L^{p (x)}$ and $W^{k, p (x)}$ , Czechoslov. Math. J., Volume 41 (1991), pp. 592-618

[11] Muckenhoupt, B.; Wheeden, R. Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., Volume 192 (1974), pp. 261-274

[12] Nakai, E.; Sawano, Y. Hardy spaces with variable exponents and generalized Campanato spaces, J. Funct. Anal., Volume 262 (2012), pp. 3665-3748

[13] Peetre, J. On the theory of $L_{p, λ}$ spaces, J. Funct. Anal., Volume 4 (1969), pp. 71-87

[14] Sobolev, S. On a theorem of functional analysis, Mat. Sb., Volume 46 (1938) no. 4, pp. 471-497

[15] Tan, J.; Liu, Z. Homogeneous fractional integrals on variable exponent function spaces, Acta Math. Sin. (Chin. Ser.), Volume 58 (2015) no. 2, pp. 309-320

[16] Tan, J.; Zhao, J. Fractional integrals on variable Hardy–Morrey spaces, Acta Math. Hung. (2015) (in press)

[17] Wang, H. Boundedness of fractional integral operators with rough kernels on weighted Morrey spaces, Acta Math. Sin. (Chin. Ser.), Volume 56 (2013) no. 2, pp. 175-186

[18] Xu, J. Variable Besov and Triebel–Lizorkin spaces, Ann. Acad. Sci. Fenn., Math., Volume 33 (2008) no. 2, pp. 511-522

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