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Estimates for the Products of the Green Function and the Martin Kernel

Published online by Cambridge University Press:  11 January 2016

Kentaro Hirata
Kentaro Hirata*
Affiliation:
Faculty of Education and Human Studies, Akita University, Akita 010-8502, Japan, hirata@math.akita-u.ac.jp
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Abstract

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Let Ω be a proper subdomain of ℝn, n ≥ 2, and let x0∈ Ω be fixed. By GΩ and KΩ we denote the Green function and the Martin kernel for Ω, respectively. Under a certain assumption on Ω near a boundary point ξ, we show that the product GΩ(x, x0)KΩ(x, ξ) is comparable to |x - ξ|2-n for x in a nontangential cone with vertex at ξ. We also give an estimate for the product KΩ(x, ξ)KΩ(x,η) in a uniform domain, where η is another boundary point.

Keywords

31B25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 188 , December 2007 , pp. 1 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

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