Boundary properties of Green functions in the plane

DOI10.1215/00127094-2008-044zbMath1157.35327arXivmath/0608493OpenAlexW2024212270WikidataQ59288420 ScholiaQ59288420MaRDI QIDQ953961

Anton D. Baranov, Haakan Hedenmalm

Publication date: 7 November 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608493

zbMATH Keywords

bounded simply connected plane domainsGrunsky identityuniform Sobolev embedding theorem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) General theory of conformal mappings (30C35) Capacity and harmonic measure in the complex plane (30C85) General theory of univalent and multivalent functions of one complex variable (30C55)

Related Items (13)

Bounds on the growth of subharmonic frequently oscillating functions ⋮ On \(L^1\)-estimates of derivatives of univalent rational functions ⋮ Norm estimates of the Cauchy transform and related operators ⋮ Analysis on quasidisks: a unified approach through transmission and jump problems ⋮ Cauchy transform and Poisson's equation ⋮ Spectral notions for conformal maps: a survey ⋮ On Hörmander's solution of the \(\bar{\partial}\)-equation. I ⋮ Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator ⋮ Bloch functions and asymptotic tail variance ⋮ Sharpening Hölder's inequality ⋮ \(L^p\rightarrow L^q\) norm estimates of Cauchy transforms on the Dirichlet problem and their applications ⋮ \(L^p\)-theory for Cauchy-transform on the unit disk ⋮ Gaussian analytic functions and operator symbols of Dirichlet type

Cites Work

• Spectral notions for conformal maps: a survey
• Extremal inequalities in Sobolev spaces and quasiconformal mappings
• On coefficient problems for univalent functions and conformal dimension
• Weighted Bergman spaces and the integral means spectrum of conformal mappings
• Density properties of harmonic measure
• On certain lemmas of Marcinkiewicz and Carleson
• On the universal integral means spectrum of conformal mappings near the origin
• Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in L^p(C)
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