Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in Lp(·)(Γ). (2nd February 2005) - Kokilashvili, V.; Paatashvili, V.; Samko, S.
Abstract : We study the Riemann boundary value problemΦ + ( t ) = G ( t ) Φ − ( t ) + g ( t ), for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spacesL p ( · ) ( Γ ) with variable exponent. We consider both the case when the coefficientG is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.