Admissible convergence of Poisson integrals in symmetric spaces
type: Item
instance of: scholarly article
title: Admissible convergence of Poisson integrals in symmetric spaces
zbMATH Open document ID: 0646.31008
DOI: 10.2307/1971281
author: Peter Sjögren
published in: Annals of Mathematics. Second Series
publication date: 1986-01-01T00:00:00Z
review text: Let f be an \(L^ p\) function, \(p>1\), on the distinguished boundary of a Furstenberg-Satake compactification of a symmetric space. We prove that the Poisson integral Pf of f converges admissibly at almost all components of each boundary of the compactification. This was known previously only for large p. In particular, Pf converges admissibly to f almost everywhere at the distinguished boundary. A similar result is obtained for the normalized \(\lambda\)-Poisson integral \({\mathcal P}_{\lambda}f\). The method of proof uses maximal functions, and it also gives a new proof of almost everywhere restricted convergence of Pf and \({\mathcal P}_{\lambda}f\) for \(f\in L^ 1\).
Mathematics Subject Classification ID: 31C12
Mathematics Subject Classification ID: 31B10
zbMATH DE Number: 4054023
zbMATH Keywords: Furstenberg-Satake compactification
zbMATH Keywords: symmetric space
zbMATH Keywords: Poisson integral
zbMATH Keywords: boundary of the compactification
zbMATH Keywords: maximal functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971281
OpenAlex ID: W2312383609
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description: scientific article; zbMATH DE number 4054023