Abstract
We study composition operators on a class of bounded domains including convex domains \({\Omega \subset {{\mathbb{C}}^n}}\). We show that a general self-map \({\phi}\) of \({\Omega}\) always induces a bounded operator \({C_\phi: A^p_\alpha(\Omega) \to A^p_{\alpha+n-1}(\Omega)}\) and the weight gain \({n-1}\) is optimal in certain sense. When \({\phi}\) is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.
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H. Koo was supported by NRF of Korea (2014R1A1A2054145).
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Koo, H., Li, SY. Composition Operators on Bounded Convex Domains in \({{\mathbb{C}}^n}\) . Integr. Equ. Oper. Theory 85, 555–572 (2016). https://doi.org/10.1007/s00020-016-2300-7
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DOI: https://doi.org/10.1007/s00020-016-2300-7