Dirichlet's problem on Green lines and some convergence theorems for Denjoy's domains
type: Item
instance of: scholarly article
title: Dirichlet's problem on Green lines and some convergence theorems for Denjoy's domains
zbMATH Open document ID: 0789.31002
DOI: 10.1007/BF03025719
author: V. Pereyra
published in: Mathematische Zeitschrift
publication date: 1994-04-12T00:00:00Z
full work available at URL: https://eudml.org/doc/174527
review text: The author proves a Fatou type theorem and the convergence of almost all Green lines in the Martin boundary for Denjoy domains in the plane. These are open subsets of \(\mathbb{C}\) with nonpolar boundary strictly included in \(\mathbb{R}\). For the corresponding sets in higher dimensions we prove convergence along the Green lines in the sense of \(L^ 1\) for every bounded harmonic function. The main difficulty is that we do not know the geometric behaviour of the Green lines (for example, non tangential approach at the boundary).
Mathematics Subject Classification ID: 31A20
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 31C35
zbMATH DE Number: 549769
zbMATH Keywords: convergence of Green lines
zbMATH Keywords: harmonic space
zbMATH Keywords: Poisson-Martin kernels
zbMATH Keywords: minimal positive harmonic functions
zbMATH Keywords: Fatou type theorem
zbMATH Keywords: Martin boundary
zbMATH Keywords: Denjoy domains
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549769