Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T16:19:50.004Z Has data issue: false hasContentIssue false
  • English
  • Français

BOUNDARY BEHAVIOUR OF QUOTIENTS OF MARTIN KERNELS

Published online by Cambridge University Press:  17 May 2007

Kentaro Hirata
Kentaro Hirata
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan (hirata@math.sci.hokudai.ac.jp)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given two intersecting domains, we investigate the boundary behaviour of the quotient of Martin kernels of each domain. To this end, we give a characterization of minimal thinness for a difference of two subdomains in terms of Martin kernels of each domain. As a consequence of our main theorem, we obtain the boundary growth of the Martin kernel of a Lipschitz domain, which corresponds to earlier results for the boundary decay of the Green function for a Lipschitz domain investigated by Burdzy, Carroll and Gardiner.

Keywords

Primary 31B0531B2531C35boundary behaviourMartin kernelminimal thinness
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 2 , June 2007 , pp. 377 - 388
Copyright
Copyright © Edinburgh Mathematical Society 2007