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arXiv · 2007.04907

Compact differences of composition operators on Bergman spaces induced by doubling weights

Bin Liu·Jouni Rättyä·Fanglei Wu
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Abstract

Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_\omega$ to the Lebesgue space $L^q_\nu$, where $0 q$ and $\omega\in\mathcal{D}$, involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of $q$-Carleson measures for the classical weighted Bergman space $A^p_\alpha$ with $-1<\alpha<\infty$ to the setting of doubling weights. The case $\omega\in\widehat{\mathcal{D}}$ is also briefly discussed and an open problem concerning this case is posed.

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Bin Liu, Jouni Rättyä, Fanglei Wu. 2020-07-09. Compact differences of composition operators on Bergman spaces induced by doubling weights. https://arxiv.org/abs/2007.04907

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