Maximal, singular and potential operators in generalized variable exponent Morrey spaces
We consider generalized Morrey spaces with variable exponent and a general function defining the Morrey-type norm. In case of bounded domains we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev-Adams type for the Riesz-type potential operator, also of variable order. The conditions for the boundedness are given it terms of Zygmund-type integral inequalities which do not assume any kind of monotonicity condition in the variable. The latter makes the results new even in the case of constant .
The talk is based on a joint paper with V. Guliev and M. Hajibayev.
