Interpolating sequences and embedding theorems in weighted Bergman spaces
type: Item
instance of: scholarly article
title: Interpolating sequences and embedding theorems in weighted Bergman spaces
zbMATH Open document ID: 0867.30025
author: Masahiro Yamada
published in: Hokkaido Mathematical Journal
publication date: 1997-05-19T00:00:00Z
review text: For \(0<p<\infty\), let \(L^p_a(\mu)\) denote the weighted Bergman space on the unit disk \(D\) in the complex plane, where \(\mu\) is a finite positive Borel measure on \(D\). When \(\mu\) is an absolutely continuous measure which satisfies an \((A_p)\)-condition, we study interpolating sequences on \(L^p_a (\mu)\) and give several sufficient conditions in order that such a sequence exists in \(L^p_a (\mu)\). Using them, we obtain embedding theorems for weighted Bergman spaces between \(L^p_a (\mu)\) and \(L^q_a (\nu)\), where \(\nu\) is a finite positive Borel measure on \(D\) and \(0<q <\infty\).
Mathematics Subject Classification ID: 30D99
Mathematics Subject Classification ID: 42A50
zbMATH DE Number: 1011282
zbMATH Keywords: \(A_ p\)-condition
zbMATH Keywords: interpolation sequences
zbMATH Keywords: Carleson inequality
zbMATH Keywords: Bergman spaces
reviewed by: Takahiko Nakazi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351516748
OpenAlex ID: W2125877900
DOI: 10.14492/HOKMJ/1351516748
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description: scientific article; zbMATH DE number 1011282