Abstract
ABSTRACTIn this paper we prove the boundedness of certain sublinear operators , , generated by fractional integral operators with rough kernels , , from one generalized local Morrey space to another , , , and from the space to the weak space , , . In the case b belongs to the local Campanato space and is a linear operator, we find the sufficient conditions on the pair which ensures the boundedness of the commutator operators from to , , , , . In all cases the conditions for the boundedness of are given in terms of Zygmund-type integral inequalities on , which do not assume any assumption on monotonicity of in r.
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