Functional Analysis and Applications Seminar 

12/10/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Stefan Samko, Universidade do Algarve, Faro

Classical operators of harmonic analysis in Lorentz spaces with variable exponent

We introduce the Lorentz space \(L_{p,q}\) with variable exponents \(p(t), q(t)\) and prove the boundedness of the maximal, singular integral and potential type operators in these spaces. The main goal is to show that the boundedness of these operators in the spaces \(L_{p,q}\) is possible without the local \(\log\)-condition on the exponents, typical for the variable exponent Lebesgue spaces; instead the exponents \(p(t)\) and \(q(t)\) should only satisfy decay conditions of \(\log\)-type as \(t\) tends to \(0\) and infinity. To prove this, we base ourselves on the recent progress in the problem of the validity of Hardy inequalities in variable exponent Lebesgue spaces.

The talk is based on a joint paper with V. Kokilashvili.