Imbedding of Bergman spaces
type: Item
instance of: scholarly article
title: Imbedding of Bergman spaces
zbMATH Open document ID: 0647.30029
DOI: 10.1007/BF00966193
published in: Lithuanian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: For \(0<p<\infty\), \(\alpha\geq 1\) the author obtains necessary and sufficient conditions for a measure \(\mu\) in order that the Bergman space \(A^ p\) could be imbedded into the Lorentz space \(L^{\alpha p,p}(\mu)\). As a corollary, a Bergman space analogue of the Fejér-Riesz theorem is obtained. Methods used in the paper are similar to those used by \textit{E. Amar} and \textit{A. Bonami} [Bull. Soc. Math. France 107, 23-48 (1979; Zbl 0409.46035)], \textit{W. W. Hastings} [Proc. Am. Math. Soc. 52, 237-241 (1975; Zbl 0296.31009)], \textit{J. A. Cima} and \textit{W. R. Wogen} [J. Oper. Theory 7, 157-163 (1982; Zbl 0499.42011)] and \textit{D. Luecking} [Proc. Am. Math. Soc. 87, 656-660 (1983; Zbl 0521.32005)].
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 4055998
zbMATH Keywords: Carleson's imbedding theorem
zbMATH Keywords: pseudo hyperbolic metric
zbMATH Keywords: Bergman space
zbMATH Keywords: Lorentz space
author: A. Zabulenis
reviewed by: Dmitry Khavinson
MaRDI profile type: Publication
cites work: Q3329691
cites work: Q3205523
cites work: Mesures de Carleson d'ordre $\alpha$ et solutions au bord de l'équation $\overline\partial$
cites work: Interpolations by bounded analytic functions and the corona problem
cites work: Q3965067
cites work: Extension of a theorem of Carleson
cites work: A Carleson Measure Theorem for Bergman Spaces
cites work: A Technique for Characterizing Carleson Measures on Bergman Spaces
description: scientific article; zbMATH DE number 4055998