The Riemann and Dirichlet Problems with Data from the Grand Lebesgue Spaces

DOI10.1007/978-3-0348-0516-2_13zbMath1276.47039OpenAlexW36735809MaRDI QIDQ4912919

Vakhtang Paatashvili, Vakhtang Kokilashvili

Publication date: 28 March 2013

Published in: Advances in Harmonic Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0516-2_13

zbMATH Keywords

Dirichlet problemRiemann boundary value problemgrand Lebesgue spaceCauchy type integralpiecewise continuous coefficientpiecewise smooth boundaryLyapunov contour

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Linear operators on function spaces (general) (47B38) Inequalities for sums, series and integrals (26D15)

Related Items

The Riemann-Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue spaces ⋮ Riemann–Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue Spaces

Cites Work

• Boundedness criteria for singular integrals in weighted Grand Lebesgue spaces
• The Dirichlet problem for harmonic functions from variable exponent Smirnov classes in domains with piecewise smooth boundary
• The Riemann--Hilbert problem and the generalized Neumann kernel
• Lebesgue and Sobolev spaces with variable exponents
• The Riemann-Hilbert problem in weighted classes of Cauchy type integrals with density from \(L^{P(\cdot)}(\Gamma)\)
• On the integrability of the Jacobian under minimal hypotheses
• The method of Cauchy-type integrals in discontinuous boundary value problems of the theory of holomorphic functions of a complex variable
• Inverting the \(p\)-harmonic operator
• Carleson curves, Muckenhoupt weights, and Toeplitz operators
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• Boundedness of weighted singular integral operators in grand Lebesgue spaces
• The maximal theorem for weighted grand Lebesgue spaces
• Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent
• Factorization and extrapolation of weights
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