Author

Li He

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Preprint Sep 2026

Closed Range and Essential Norms of Composition Operators on Weighted Dirichlet Spaces

We study closed range and essential norms of bounded composition operators $C_\varphi$ on weighted Dirichlet spaces $\mathcal{D}_{\alpha}$. For $-1<\alpha<0$, we first consider maps whose images are obtained by removing a compact subset from a simply connected subdomain of $\mathbb{D}$. In this setting, closed range is...

Cai-Xing Gu, Li He, Xiao-Feng Wang et al. · 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