Integral-type operators acting between weighted-type spaces on the unit ball
type: Item
instance of: scholarly article
title: Integral-type operators acting between weighted-type spaces on the unit ball
zbMATH Open document ID: 1197.47061
author: Stevo Stević
author: Sei-Ichiro Ueki
published in: Applied Mathematics and Computation
publication date: 2009-12-18T00:00:00Z
review text: Let \(\mathbb{B}\) denote the unit ball in \(\mathbb{C}^n\) and \(H(\mathbb{B})\) the space of all holomorphic functions on \(\mathbb{B}\). In this paper, the authors study the boundedness and compactness of the integral-type operators \[ I_\varphi^gf(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{dt}{t},\quad z\in \mathbb B, \] where \(g\in H(\mathbb{B})\), \(g(0)=0\), \(\varphi\) is a holomorphic self-map of \(\mathbb{B}\) and \(\Re f\) is the radial derivative of the function \(f\), between weighted-type spaces on the unit ball.
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 32A37
zbMATH DE Number: 5649895
zbMATH Keywords: integral-type operator
zbMATH Keywords: weighted-type space
zbMATH Keywords: radial derivative
zbMATH Keywords: essential norm
reviewed by: Pengyan Hu
MaRDI profile type: Publication
full work available at URL: j.amc.2009.08.050
OpenAlex ID: W2069783490
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DOI: 10.1016/J.AMC.2009.08.050
description: scientific article; zbMATH DE number 5649895