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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)
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Abstract

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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