Weighted Hardy and Smirnov classes and the Dirichlet problem for a ring within the framework of variable exponent analysis

DOI10.1080/17476933.2011.557153zbMath1256.30022OpenAlexW2123054696MaRDI QIDQ3094255

Vakhtang Paatashvili, Vakhtang Kokilashvili

Publication date: 21 October 2011

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2011.557153

zbMATH Keywords

Dirichlet problemCauchy integralHardy classesPoisson integralanalytic functionsharmonic functionsvariable exponent analysisSmirnov classes

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Boundary value problems in the complex plane (30E25) Linear operators on function spaces (general) (47B38) Hardy spaces (30H10)

Related Items (2)

Smirnov classes of analytic functions with variable exponent in multiply connected domains ⋮ The Dirichlet problem for harmonic functions from variable exponent Smirnov classes in domains with piecewise smooth boundary

Cites Work

• The Riemann-Hilbert problem in weighted classes of Cauchy type integrals with density from \(L^{P(\cdot)}(\Gamma)\)
• Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces
• Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in \(L^{p(\cdot)}(\Gamma)\)
• Calderón-Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics

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