Integral-type operators between \(\alpha \)-Bloch spaces and Besov spaces on the unit ball
type: Item
instance of: scholarly article
title: Integral-type operators between \(\alpha \)-Bloch spaces and Besov spaces on the unit ball
zbMATH Open document ID: 1219.47049
author: Stevo Stević
published in: Applied Mathematics and Computation
publication date: 2010-08-18T00:00:00Z
review text: Let \(H(\mathbb{B})\) denote the space of all holomorphic functions on the unit ball \(\mathbb{B}\subset\mathbb{C}\). For \(g\in H(\mathbb{B})\), the integral-type operators \(T_g\) and \(L_g\) are defined by \[ T_g(f)(z)=\int_0^1f(tz)\mathcal{R}g(tz)\frac{dt}{t} \quad{\text{and}}\quad L_g(f)(z)=\int_0^1\mathcal{R}f(tz)g(tz)\frac{dt}{t}, \quad z\in\mathbb{B}, \] where \(\mathcal{R}h\) is the radial derivative of \(h\). In this paper, the author characterizes the boundedness and compactness of \(T_g\) and \(L_g\) between \(\alpha\)-Bloch spaces and Besov spaces on the unit ball.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 32A37
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 5772432
zbMATH Keywords: \(\alpha\)-Bloch space
zbMATH Keywords: Besov space
zbMATH Keywords: integral-type operator
zbMATH Keywords: boundedness
zbMATH Keywords: compactness
zbMATH Keywords: radial derivative
zbMATH Keywords: Hadamard gap
reviewed by: Pengyan Hu
MaRDI profile type: Publication
full work available at URL: j.amc.2010.04.074
OpenAlex ID: W1965980647
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DOI: 10.1016/J.AMC.2010.04.074
description: scientific article; zbMATH DE number 5772432