Boundary properties of Green functions in the plane
2008 (English)In: Duke mathematical journal, ISSN 0012-7094, Vol. 145, no 1, 1-24 p.Article in journal (Refereed) Published
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 p = 2 of a more general Grunsky identily for L-p-spaces.
Place, publisher, year, edition, pages
2008. Vol. 145, no 1, 1-24 p.
IdentifiersURN: urn:nbn:se:kth:diva-17854DOI: 10.1215/00127094-2008-044ISI: 000259668300001ScopusID: 2-s2.0-54149102794OAI: oai:DiVA.org:kth-17854DiVA: diva2:335899
QC 201005252010-08-052010-08-05Bibliographically approved