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math.FA2026
Compactness of Toeplitz Operators on the Bergman Space
Guangfu Cao, Li He, Shuqing Zhang
Let $φ\in L^\infty(\D)$. We study compactness criteria for \(T_φ\) on the Bergman space $A^2(\D)$. Axler and Zheng~\cite{AZ1998} established a necessary and sufficient condition fo…
math.FA2026
Closed Range and Essential Norms of Composition Operators on Weighted Dirichlet Spaces
Caixing Gu, Li He, Xiaofeng Wang +1
We study closed range and essential norms of bounded composition operators on weighted Dirichlet spaces . For , we first consider maps whose images are…
math.CV2026
The Reciprocal Problem on Weighted Bergman Spaces
Guangfu Cao, Li He, Shuqing Zhang
We study the reciprocal problem for weighted Bergman spaces: if $f\in A_α^p(\Bn)$ and $\inf_{\Bn}|f|>0$, does it follow that $1/f\in A_α^p(\Bn)$? We determine the range of paramete…