Carleson conditions in Bergman-Orlicz spaces
type: Item
instance of: scholarly article
title: Carleson conditions in Bergman-Orlicz spaces
zbMATH Open document ID: 1251.30007
author: Armando García Ortiz
author: Julio C. Ramos Fernández
published in: Complex Analysis and Operator Theory
publication date: 2010-10-04T00:00:00Z
review text: Let \(\varphi:[0,\infty)\to [0,\infty)\) be a continuous, increasing function with \(\varphi(0)=0\) and \(\lim_{t\to \infty}\varphi(t)=\infty\). Let \(\mathbb D\) denote the open unit disk in \(\mathbb C\). The Bergman-Orlicz space \(A^\varphi\) is the set of all holomorphic functions \(f\) on \(\mathbb D\) with \[ \int_{\mathbb D}\varphi(\lambda|f(z)|)dm(z)<\infty \] for some positive constant \(\lambda\) depending on \(f\). \(A^\varphi\) is a generalization of the classical Bergman space \(A^p\). The paper under review gives characterizations of (forward and reverse) Carleson conditions in terms of inequalities that involve functions in the Bergman-Orlicz space, which generalizes two important results from the theory of Bergman spaces to the context of Bergman-Orlicz spaces.
Mathematics Subject Classification ID: 30C25
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 5795254
zbMATH Keywords: Bergman-Orlicz spaces
zbMATH Keywords: \({\mathcal{N}}\)-function
zbMATH Keywords: Carleson conditions
zbMATH Keywords: pseudohyperbolic disks
reviewed by: Zengjian Lou
MaRDI profile type: Publication
full work available at URL: s11785-009-0010-8
OpenAlex ID: W2036943041
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DOI: 10.1007/S11785-009-0010-8
description: scientific article; zbMATH DE number 5795254