30/11/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Vakhtang Kokilashvili, A. Razmadze Mathematical Institute, Tbilisi, Georgia
Singular integrals in weighted Lebesgue spaces with variable
exponent and applications
The goal of the talk is to present the boundedness criteria for
singular integrals in weighted Lebesgue spaces with variable
exponent. The following topics will be discussed: boundedness of
the generalized singular integrals on Carleson curves arising in
the theory of I. N. Vekua's generalized analytic functions;
sufficient conditions and examples of a couple of weights ensuring
two-weight estimates for singular integrals and maximal functions
in variable Lebesgue spaces; applications to the Dirichlet boundary
value problem in "bad" domains and to the problem of the mean
summability of Fourier trigonometric series in non-standard,
two-weight setting.