Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel

By Vagif S. Guliyev. Journal of Mathematical Sciences, 2012

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Let MΩ,α and IΩ,α be the fractional maximal and integral operators with rough kernels, where 0 < α < n. We study the continuity properties of MΩ,α and IΩ,α on the generalized local Morrey spaces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ LM_{{p,\varphi}}^{{\left\{ {{x_0}} \right\}}} $$\end{document} . We prove that the commutators of these operators with local Campanato functions are bounded. Bibliography: 34 titles.

Subfields: Applied Mathematics

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