Abstract
Let be the Banach space of holomorphic functions on the open unit disk in the complex plane consisting of those such that and be the closed subspace of consisting of those for which , where is any nonnegative integer and . We give boundedness characterizations, norm estimates and essential norm estimates of weighted composition operators and , respectively, where . As a corollary, we characterize the compactness of . Specifically, our characterizations involve not only the classical Julia–Carathéodory type condition, but also the powers . In addition, our results extend several well-known results in the literature.
Citation
Maofa Wang. Shuming Wang. "Weighted composition operators between -th -weighted spaces." Rocky Mountain J. Math. 51 (4) 1503 - 1519, August 2021. https://doi.org/10.1216/rmj.2021.51.1503
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