## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Products of composition and differentiation operators on the weighted Bergman space

Stevo Stević

#### 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

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