Author

Shu-Qing Zhang

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Preprint Sep 2026

The Reciprocal Problem on Weighted Bergman Spaces

We study the reciprocal problem for weighted Bergman spaces: if $f\in A_\alpha^p(\Bn)$ and $\inf_{\Bn}|f|>0$, does it follow that $1/f\in A_\alpha^p(\Bn)$? We determine the range of parameters for which the answer is affirmative. In particular, we prove that functions in $A_{\alpha}^p(\D)$ have the reciprocal property...

Guang-Fu Cao, Li He, Shu-Qing Zhang · 0 citations

Preprint Sep 2026

Compactness of Toeplitz Operators on the Bergman Space

Let $\varphi\in L^\infty(\D)$. We study compactness criteria for $T_\varphi$ on the Bergman space $A^2(\D)$. Axler and Zheng~\cite{AZ1998} established a necessary and sufficient condition for compactness in terms of the Berezin transform. For a general bounded measurable function $\varphi$, however, its Berezin trans...

Guang-Fu Cao, Li He, Shu-Qing Zhang · 0 citations