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1 October 2008 Boundary properties of Green functions in the plane
Anton Baranov, Håkan Hedenmalm
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Duke Math. J. 145(1): 1-24 (1 October 2008). DOI: 10.1215/00127094-2008-044

Abstract

We study the boundary properties of the Green function of bounded simply connected domains in the plane. Essentially, this amounts to studying the conformal mapping taking the unit disk onto the domain in question. Our technique is inspired by a 1995 article of Jones and Makarov [11]. The main tools are an integral identity as well as a uniform Sobolev embedding theorem. The latter is in a sense dual to the exponential integrability of Marcinkiewicz-Zygmund integrals. We also develop a Grunsky identity, which contains the information of the classical Grunsky inequality. This Grunsky identity is the case where p=2 of a more general Grunsky identity for Lp-spaces

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Anton Baranov. Håkan Hedenmalm. "Boundary properties of Green functions in the plane." Duke Math. J. 145 (1) 1 - 24, 1 October 2008. https://doi.org/10.1215/00127094-2008-044

Information

Published: 1 October 2008
First available in Project Euclid: 17 September 2008

zbMATH: 1157.35327
MathSciNet: MR2451287
Digital Object Identifier: 10.1215/00127094-2008-044

Subjects:
Primary: 30C35 , 35B65
Secondary: 30C55 , 30C85

Rights: Copyright © 2008 Duke University Press

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Vol.145 • No. 1 • 1 October 2008
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