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Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

Boundary Value Problems volume 2005, Article number: 361409 (2005) Cite this article

Abstract

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.

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Authors and Affiliations

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

    V Kokilashvili & V Paatashvili

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

    S Samko

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  1. V Kokilashvili
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  2. V Paatashvili
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  3. S Samko
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Correspondence to V Kokilashvili.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kokilashvili, V., Paatashvili, V. & Samko, S. Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in. Bound Value Probl 2005, 361409 (2005). https://doi.org/10.1155/BVP.2005.43

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  • DOI: https://doi.org/10.1155/BVP.2005.43