On an Extension of Stević–Sharma Operator from the General Space to Weighted-Type Spaces on the Unit Ball

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• 作者：Yongmin Liu ; Yanyan Yu
• 关键词：Multiplication operator ; Composition operator ; Radial derivative ; The general space ; Weighted ; type spaces
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：11
• 期：2
• 页码：261-288
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Operator Theory; Analysis;
• 出版者：Springer International Publishing
• ISSN：1661-8262
• 卷排序：11

文摘

Let \(H({\mathbb {B}})\) denote the space of all holomorphic functions on the unit ball \({\mathbb {B}}\) of \( {\mathbb {C}}^n\), \(\psi _1,\psi _2,\psi _3\in H({\mathbb {B}}) \) and \(\varphi \) be a holomorphic self-map of \( {\mathbb {B}}\). This paper studies the boundedness and compactness of the following extension of the Stević–Sharma operator, recently proposed by Liu and Yu $$\begin{aligned} T_{\psi _1, \psi _2, \psi _3,\varphi }f(z)=\psi _1(z)f(\varphi (z))+\psi _2(z){{\mathcal {R}}}f(\varphi (z))+\psi _3(z){{\mathcal {R}}}\left( f\circ \varphi \right) (z), z\in {\mathbb {B}}, \end{aligned}$$where \({{\mathcal {R}}}f(z)\) is the radial derivative of \(f\) at \(z\), from the general space \(F(p, q, s)\) to the weighted-type space \(H_{\mu }^\infty \) or the little weighted-type space \(H_{\mu ,0}^\infty \) on the unit ball.KeywordsMultiplication operatorComposition operatorRadial derivativeThe general spaceWeighted-type spacesCommunicated by Daniel Aron Alpay.