Duke Mathematical Journal
- Duke Math. J.
- Volume 145, Number 1 (2008), 1-24.
Boundary properties of Green functions in the plane
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 . 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 of a more general Grunsky identity for -spaces
Duke Math. J., Volume 145, Number 1 (2008), 1-24.
First available in Project Euclid: 17 September 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B65: Smoothness and regularity of solutions 30C35: General theory of conformal mappings
Secondary: 30C55: General theory of univalent and multivalent functions 30C85: Capacity and harmonic measure in the complex plane [See also 31A15]
Baranov, Anton; Hedenmalm, Håkan. Boundary properties of Green functions in the plane. Duke Math. J. 145 (2008), no. 1, 1--24. doi:10.1215/00127094-2008-044. https://projecteuclid.org/euclid.dmj/1221656860