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arXiv · 1811.01385

Weighted composition operators on weighted Bergman spaces induced by double weights

Juntao Du·Songxiao Li·Yecheng Shi
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Abstract

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi$ on Bergman type spaces $A_\omega^p $ with double weight $\omega$. Let $X=\{u\in H(D): uC_\varphi:A_\omega^p\to A_\omega^p \mbox{ is bounded}\}.$ For some regular weights $\omega$, we obtain that $X=H^\infty$ if and only if $\varphi$ is a finite Blaschke product.

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Juntao Du, Songxiao Li, Yecheng Shi. 2018-11-04. Weighted composition operators on weighted Bergman spaces induced by double weights. https://arxiv.org/abs/1811.01385

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