Norm estimates of the Cauchy transform and related operators

DOI10.1016/j.jfa.2020.108726zbMath1446.42024arXiv2008.02524OpenAlexW3046939358MaRDI QIDQ2197814

Jian-Feng Zhu, David Kalaj

Publication date: 1 September 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.02524

zbMATH Keywords

Cauchy transformBergman projectionhypergeometric functionBessel function

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items

Norm estimates for a class of operators related to the Bergman projection ⋮ Some estimates for the Cauchy transform in higher dimensions ⋮ Schwarz type lemmas for generalized harmonic functions ⋮ \(L^p\)-theory for Cauchy-transform on the unit disk ⋮ Schwarz lemma for solutions of the \(\alpha\)-harmonic equation ⋮ Bergman projections, Berezin transforms and Cauchy transform on exponential Orlicz spaces and Lorentz-Zygmund spaces

Cites Work

• On some integral operators related to the Poisson equation
• Cauchy transform and Poisson's equation
• Norm estimate of the Cauchy transform on \(L^p(\Omega)\)
• Boundary properties of Green functions in the plane
• Bloch space and the norm of the Bergman projection
• Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
• The Cauchy Transform on Bounded Domains
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