1687-2770-2005-361409 1687-2770 Research Article <p>Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in <inline-formula><graphic file="1687-2770-2005-361409-i1.gif"/></inline-formula></p>KokilashviliVkokil@rmi.acnet.gePaatashviliVpaata@rmi.acnet.geSamkoSssamko@ualg.pt

A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi 380093, Georgia

Faculty of Science and Technology, University of Algarve, Faro 8000, Portugal

Boundary Value Problems1687-2770200520051361409http://www.boundaryvalueproblems.com/content/2005/36140910.1155/BVP.2005.43 972004222005 2005Kokilashvili et al.

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient 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.