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.