An integral formula in weighted Bergman spaces
type: Item
instance of: scholarly article
title: An integral formula in weighted Bergman spaces
zbMATH Open document ID: 1198.30052
DOI: 10.1007/BF03321767
author: Rachel Weir
published in: Computational Methods and Function Theory
publication date: 2010-06-17T00:00:00Z
review text: This paper is best described by its abstract: ``In order to establish that extremal functions in the Bergman space \(A^p\) act as both expansive multipliers and contractive divisors, \textit{P. Duren, D. Khavinson, H. S. Shapiro} and \textit{C. Sundberg} [Pac. J. Math. 157, No.1, 37--56 (1993; Zbl 0739.30029)] made use of an integral formula involving the biharmonic Green function. Using a weighted biharmonic Green function, we derive an analogous integral formula in the standard weighted Bergman space \(A^p_\alpha\) when \(\alpha=1\), and we also discuss how the formula can be established for general \(\alpha\). Moreover, we show that each \(A^p_1\)-inner function acts as a contractive divisor on the invariant subspace which it generates.''
reviewed by: Raymond Mortini
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 31A30
zbMATH DE Number: 5723312
zbMATH Keywords: Bergman space
zbMATH Keywords: biharmonic Green function
zbMATH Keywords: extremal function
zbMATH Keywords: contractive divisor
zbMATH Keywords: expansive multiplier
zbMATH Keywords: inner function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5723312