Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel

Abstract

Let M Ω,α and I Ω,α be the fractional maximal and integral operators with rough kernels, where 0 < α < n. We study the continuity properties of M Ω,α and I Ω,α on the generalized local Morrey spaces $$ LM_{{p,\varphi}}^{{\left\{ {{x_0}} \right\}}} $$ . We prove that the commutators of these operators with local Campanato functions are bounded. Bibliography: 34 titles.