Densité de l'intégrale d'aire dans \({\mathbb{R}}_+^{n+1}\) et limites non tangentielles. (Density of the area integral in \({\mathbb{R}}_ +^{n+1}\) and non-tangential limits)
type: Item
instance of: scholarly article
title: Densité de l'intégrale d'aire dans \({\mathbb{R}}_+^{n+1}\) et limites non tangentielles. (Density of the area integral in \({\mathbb{R}}_ +^{n+1}\) and non-tangential limits)
zbMATH Open document ID: 0655.31004
DOI: 10.1007/BF01394335
author: Jean Brossard
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143599
review text: Let u be a harmonic function in the half space \({\mathbb{R}}_+^{n+1}\). Let \(r\mapsto D\) r be the density of the area integral associated with u. The two main results of this paper are: -- A continuity property of the application \(r\mapsto D^ r\) (the analytic analogue of Trotter's theorem on the continuity of the local time associated with a martingale). -- A criterion for u to have a non-tangential limit, using the density of the area integral.
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 4069286
zbMATH Keywords: harmonic
zbMATH Keywords: density
zbMATH Keywords: area integral
zbMATH Keywords: continuity property
zbMATH Keywords: Trotter's theorem
zbMATH Keywords: martingale
zbMATH Keywords: non-tangential limit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4069286