Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel

Abstract

Let M ?,? and I ?,? be the fractional maximal and integral operators with rough kernels, where 0 < ? < n. We study the continuity properties of M ?,? and I ?,? on the generalized local Morrey spaces LMp,?{x0}. We prove that the commutators of these operators with local Campanato functions are bounded. Bibliography: 34 titles. © 2013 Springer Science+Business Media New York.