23/10/2009, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática Stefan Samko, Universidade do Algarve, Faro
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.