Positive kernel functions and Bergman spaces
type: Item
instance of: scholarly article
title: Positive kernel functions and Bergman spaces
zbMATH Open document ID: 0659.32010
author: Nozomu Mochizuki
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: Using the positive (``Poisson-like'') reproducing kernel for the weighted Bergman spaces \(A^{p,\delta}({\mathbb{B}})\), the author obtains Hardy- Littlewood inequalities for functions in these spaces. Similar results are obtained in the setting of the generalized half plane in \({\mathbb{C}}^ n\). As an application, the author treats the Mackey topology on \(A^{p,\delta}({\mathbb{B}})\), \(0<p<1\) and extends a one variable result due to \textit{J. Shapiro} [Duke Math. J. 43, 187-202 (1976; Zbl 0354.46036)].
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4077693
zbMATH Keywords: weighted Bergman spaces
zbMATH Keywords: Hardy-Littlewood inequalities
zbMATH Keywords: Mackey topology
reviewed by: Emil J. Straube
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227988
OpenAlex ID: W2024838503
cites work: Q3965067
cites work: Q5568718
cites work: Mean Values of Subharmonic Functions on Half-Spaces
cites work: On the Rate of Growth of Mean Values of Holomorphic and Harmonic Functions
cites work: Q4051162
cites work: A Technique for Characterizing Carleson Measures on Bergman Spaces
cites work: Inequalities of Fejér-Riesz and Hardy-Littlewood
cites work: Q3958740
cites work: Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Berman spaces
DOI: 10.2748/TMJ/1178227988
description: scientific article; zbMATH DE number 4077693