Bulletin of the Belgian Mathematical Society - Simon Stevin

Products of composition and differentiation operators on the weighted Bergman space

Stevo Stević

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 4 (2009), 623-635.

Dates
First available in Project Euclid: 9 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1257776238

Digital Object Identifier
doi:10.36045/bbms/1257776238

Mathematical Reviews number (MathSciNet)
MR2583550

Zentralblatt MATH identifier
1181.30031

Citation

Stević, Stevo. Products of composition and differentiation operators on the weighted Bergman space. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 4, 623--635. doi:10.36045/bbms/1257776238. https://projecteuclid.org/euclid.bbms/1257776238


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