The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces

DOI10.1007/978-3-0348-0648-0_17zbMath1317.42007arXiv1202.2226OpenAlexW3000002663MaRDI QIDQ5261236

Alexei Yu. Karlovich, Ilya M. Spitkovskij

Publication date: 2 July 2015

Published in: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2226

zbMATH Keywords

Hardy-Littlewood maximal operatorCauchy singular integral operatorweighted variable Lebesgue spaces\(\log\)-Hölder continuous variable exponent

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) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (23)

Weighted variable Morrey-Herz estimates for fractional Hardy operators ⋮ Algebras of convolution type operators with continuous data do not always contain all rank one operators ⋮ Approximation by Faber-Laurent rational functions in Lebesgue spaces with variable exponent ⋮ Boundedness of fractional integrals on weighted Herz spaces with variable exponent ⋮ Boundary value problems and singular integral equations on Banach function spaces ⋮ Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent ⋮ Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent ⋮ Algebras of continuous Fourier multipliers on variable Lebesgue spaces ⋮ Invertibility of Fourier convolution operators with \textit{pc} symbols on variable Lebesgue spaces with Khvedelidze weights ⋮ On local properties of singular integrals ⋮ Fourier convolution operators with symbols equivalent to zero at infinity on Banach function spaces ⋮ Semi-almost periodic Fourier multipliers on rearrangement-invariant spaces with suitable Muckenhoupt weights ⋮ Unnamed Item ⋮ Calkin images of Fourier convolution operators with slowly oscillating symbols ⋮ Commutators of the fractional Hardy operator on weighted variable Herz-Morrey spaces ⋮ Marcinkiewicz exponents and jump problem for Beltrami equation ⋮ Wavelet bases in Banach function spaces ⋮ Algebra of convolution type operators with continuous data on Banach function spaces ⋮ Measure of noncompactness of Sobolev embeddings on strip-like domains ⋮ Two weighted Herz spaces with variable exponents ⋮ Noncompactness of Fourier convolution operators on Banach function spaces ⋮ Boundedness of Pseudodifferential Operators on Banach Function Spaces ⋮ Banach algebra of the Fourier multipliers on weighted Banach function spaces

Cites Work

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• Weighted norm inequalities for the maximal operator on variable Lebesgue spaces
• Commutators of singular integrals on generalized \(L^p\) spaces with variable exponent
• Lebesgue and Sobolev spaces with variable exponents
• Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent
• Singular integral operators with piecewise continuous coefficients in reflexive rearrangement-invariant spaces
• Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces
• Perturbation theory for linear operators.
• The maximal operator in weighted variable spaces \(L^{p(\cdot)}\)
• Weighted norm inequalities for the local sharp maximal function
• Infimal convolution and Muckenhoupt \(A_{p(\cdot)}\) condition in variable \(L^p\) spaces
• The maximal operator on weighted variable Lebesgue spaces
• Singular operators in variable spaces L^{p (·)}(Ω, ρ) with oscillating weights
• Two-weighted estimations for the Hardy-Littlewood maximal function in ideal Banach spaces

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