Seminário Análise Funcional e Aplicações 

17/09/2004, 15:15 — 16:15 — Sala P3.10, Pavilhão de Matemática
Stefan Samko, Universidade do Algarve, Faro

Boundary Value Problems for Analytic Functions and Singular Operators in the Variable Exponent Spaces with General Weights

We consider the Riemann boundary value problem for analytic functions in the class of analytic functions represented by the Cauchy type integral with density in the generalized Lebesgue spaces with variable exponent. We consider both the cases when the coefficient G is piecewise continuous or it may be of a more general nature, admitting its oscillation. The solvability conditions are derived and in all the cases of solvability the explicit formulas are given. Following the approach of I.Simonenko, we make use of the results on the explicit solution of the boundary value problem to obtain the weight results for Cauchy singular integral operator in Lebesgue spaces with variable exponent, among them some extension of the well known Helson-Szego theorem.