Generalized local Morrey spaces and fractional integral operators with rough kernel

Abstract

Let $M_{Ω,\a}$ and $I_{Ω,\a}$ be the fractional maximal and integral operators with rough kernels, where $0 < \a < n$. In this paper, we shall study the continuity properties of $M_{Ω,\a}$ and $I_{Ω,\a}$ on the generalized local Morrey spaces $L{M}_{p,\phi }^{x_0}$. The boundedness of their commutators with local Campanato functions is also obtained.

arXiv admin note: text overlap with arXiv:1203.1441 by other authors