Abstract
In this paper, we study some properties of weighted composition operators on a class of weighted Bergman spaces \(A_\varphi^p\) with 0 < p ≤ ∞ and \(\varphi \in \mathcal{W}_0\). Also, we completely characterize the q-Carleson measure for \(A_\varphi^p\) in terms of the averaging function and the generalized Berezin transform with 0 < q < ∞. As applications, the boundedness and compactness of weighted composition operators acting from one Bergman space \(A_\varphi^p\) to another \(A_\varphi^q\) are equivalently described and the Schatten class property of the weighted composition operator acting on \(A_\varphi^2\) are given. Our main results are expressed in terms of certain Berezin type integral transforms.
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Supported by the National Natural Science Foundation of China (Grant Nos. 12071155, 11871170), the open project of Key Laboratory, School of Mathematical Sciences, Chongqing Normal University (Grant No. CSSXKFKTM202002) and the Innovation Research for the Postgraduates of Guangzhou University (Grant No. 2020GDJC-D08). We are co-first authors.
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Cao, G.F., He, L. & Zhang, Y.Y. Weighted Composition Operators between Bergman Spaces with Exponential Weights. Acta. Math. Sin.-English Ser. 38, 2231–2252 (2022). https://doi.org/10.1007/s10114-022-2048-8
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DOI: https://doi.org/10.1007/s10114-022-2048-8