On the boundary limits of Green potentials of functions
type: Item
instance of: scholarly article
title: On the boundary limits of Green potentials of functions
zbMATH Open document ID: 0695.31006
author: Yoshihiro Mizuta
published in: Journal of the Mathematical Society of Japan
publication date: 1988-01-01T00:00:00Z
review text: Let \(D=\{x\in R^ n:\) \(x_ n>0\}\) and let G(x,y) be the Green function in D. For a nonnegative measurable function f on D with \[ (1)\quad \int_{D}(1+| y|)^{-n} y_ nf(y) dy<\infty. \] Put \(GF(x)=\int_{D}G(x,y)f(y)dy.\) The author studies the existence of the non-tangential limits of the Green potential Gf under the condition (1) and under an additional condition on the function f depending on a calibration function \(\omega\). Under these two conditions the author shows, extending a result of K.-O. Widman (1967), that Gf has non-tangential limits on \(\partial D\setminus E\) where E has zero Hausdorff h-measure with h depending on \(\omega\).
reviewed by: M. Vuorinen
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 31B15
zbMATH DE Number: 4138132
zbMATH Keywords: non-tangential limits
zbMATH Keywords: zero Hausdorff h-measure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04040583
OpenAlex ID: W1968910403
DOI: 10.2969/JMSJ/04040583
description: scientific article; zbMATH DE number 4138132