Seminário Análise Funcional e Aplicações 

18/04/2008, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Stefan Samko, Universidade do Algarve, Faro

Generalized potential operators in variable exponent spaces

We consider generalized potential operators on a bounded measure metric space with doubling measure satisfying the upper growth condition. Under some natural assumptions on the kernel of the potential, in terms of its almost monotonicity, we present a Sobolev type theorem on the boundedness of such potential operators from the variable exponent Lebesgue space into a certain Musielak-Orlicz space with the N-function defined by the exponent p(x) and the kernel. A reformulation of the obtained result in terms of the Matuszewska-Orlicz indices of the function kernel is also given. The talk is based on a joint paper with M. Hajiboyev (Baku).