Carleson type measures on parabolic Bergman spaces
type: Item
instance of: scholarly article
title: Carleson type measures on parabolic Bergman spaces
zbMATH Open document ID: 1100.35003
author: Masaharu Nishio
author: Masahiro Yamada
published in: Journal of the Mathematical Society of Japan
publication date: 2006-03-29T00:00:00Z
review text: The \(\alpha\)-parabolic Bergman space \(b_\alpha^p\) is the space of all \(p\)-th integrable solutions \(u\) of the parabolic equation \([\partial/\partial t+(-\Delta)^\alpha]u=0\) on the upper half-space, where \(0<\alpha\leq 1\) and \(1\leq p<\infty\). In case \(\alpha=1/2\), the space \(b_{1/2}^p\) coincides with the well-known harmonic Bergman space. The main result of this paper is the characterization of Carleson measures for the derivatives of \(b^p_\alpha\)-functions. In order to obtain such a result, the authors first establish the upper and lower estimates for the derivatives of the fundamental solution. As an application, the authors obtain a characterization of positive symbol functions of bounded Toeplitz operators on \(b^2_\alpha\) in terms of averaging functions and Berezin transforms. In case \(\alpha=1/2\), some of these results and more were known by \textit{B. R. Choe, H. Koo} and \textit{H. Yi} [Potential Anal. 17, 307--335 (2002; Zbl 1014.47014)]
reviewed by: Boo Rim Choe
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5015990
zbMATH Keywords: Toeplitz operators
zbMATH Keywords: upper and lower estimates
zbMATH Keywords: Berezin transforms
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1145287094
OpenAlex ID: W1997693435
DOI: 10.2969/JMSJ/1145287094
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description: scientific article; zbMATH DE number 5015990