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November 2009 Products of composition and differentiation operators on the weighted Bergman space
Stevo Stević
Bull. Belg. Math. Soc. Simon Stevin 16(4): 623-635 (November 2009). DOI: 10.36045/bbms/1257776238

Abstract

Motivated by a recent paper by S. Ohno we calculate Hilbert-Schmidt norms of products of composition and differentiation operators on the Bergman space $A^2_\alpha,$ $\alpha>-1$ and the Hardy space $H^2$ on the unit disk. When the convergence of sequences $(\varphi_n)$ of symbols to a given symbol $\varphi$ implies the convergence of product operators $C_{\varphi_n}D^k$ is also studied. Finally, the boundedness and compactness of the operator $C_{\varphi}D^k: A^2_\alpha\to A^2_\alpha$ are characterized in terms of the generalized Nevanlinna counting function.

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Stevo Stević. "Products of composition and differentiation operators on the weighted Bergman space." Bull. Belg. Math. Soc. Simon Stevin 16 (4) 623 - 635, November 2009. https://doi.org/10.36045/bbms/1257776238

Information

Published: November 2009
First available in Project Euclid: 9 November 2009

zbMATH: 1181.30031
MathSciNet: MR2583550
Digital Object Identifier: 10.36045/bbms/1257776238

Rights: Copyright © 2009 The Belgian Mathematical Society

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Vol.16 • No. 4 • November 2009
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