\(L^p\) continuity of projectors of weighted harmonic Bergman spaces
type: Item
instance of: scholarly article
title: \(L^p\) continuity of projectors of weighted harmonic Bergman spaces
zbMATH Open document ID: 0947.31001
author: Oscar Blasco
author: Salvador Pérez-Esteva
published in: Collectanea Mathematica
publication date: 2000-11-08T00:00:00Z
full work available at URL: https://eudml.org/doc/41461
review text: We study spaces \(A^p(w)\) consisting of harmonic functions in \(B^n\) the unit ball in \(\mathbb{R}^n\) and belonging to \(L^p(w)\), where \(dw(x)=w(1-|x|)dx\) and \(w:(0,1] \to\mathbb{R}^+\) denotes a continuous integrable function. For weights satisfying certain Dini type conditions we construct families of projections of \(L^p(w)\) onto \(A^p(w)\). We use this to get for \(1<p <\infty\) and \({1\over p}+ {1\over p'}=1\), a duality \(A^p(w)^* =A^{p'}(w')\), where \(w'\) depends on \(p\) and \(w\).
reviewed by: Oscar Blasco
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 32A36
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1454851
zbMATH Keywords: harmonic Bergman spaces
zbMATH Keywords: weights
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1454851