Functional Analysis and Applications Seminar 

23/10/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building
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 $p(x)$ and a general function $\omega (x,r)$ 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 $\omega (x,r)$ in the variable. The latter makes the results new even in the case of constant $p$.

The talk is based on a joint paper with V. Guliev and M. Hajibayev.