On an integral-type operator acting between Bloch-type spaces on the unit ball
type: Item
instance of: scholarly article
title: On an integral-type operator acting between Bloch-type spaces on the unit ball
zbMATH Open document ID: 1200.32005
DOI: 10.1155/2010/214762
author: Stevo Stević
author: Sei-Ichiro Ueki
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/229919
review text: Let \(\mathbb B\) denote the open unit ball of \(\mathbb C^n\). For a holomorphic self-map \(\varphi\) of \(\mathbb B\) and a holomorphic function \(g\) in \(\mathbb B\) with \(g(0)=0\), we define the following integral-type operator: \(I_\varphi^g f(z)=\int^1_0 \Re f(\varphi(tz))g(tz)(dt/t)\), \(z\in\mathbb B\). Here \(\Re f\) denotes the radial derivative of a holomorphic function \(f\) in \(\mathbb B\). We study the boundedness and compactness of the operator between Bloch-type spaces \({\mathcal B}\omega\) and \({\mathcal B}\mu\), where \(\omega\) is a normal weight function and \(\mu\) is a weight function. Also, we consider the operator between the little Bloch-type spaces \({\mathcal B}_{\omega,0}\) and \({\mathcal B}_{\mu,0}\).
Mathematics Subject Classification ID: 32A37
zbMATH DE Number: 5791606
MaRDI profile type: Publication
OpenAlex ID: W2027051787
Wikidata QID: Q58649775
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description: scientific article; zbMATH DE number 5791606