Functional Analysis and Applications Seminar 

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.