Abstract
We determine the norm of a weighted composition operator \(W_{\psi ,\varphi }\), acting on the Hardy space \(H^{2}\) or one of the weighted Bergman spaces \(A_{\alpha }^{2}\), in the case where the composition symbol \(\varphi \) is an automorphism of the unit disk. Furthermore, we characterize all such operators that have maximal norm relative to an upper bound stated in terms of \(\Vert \psi \Vert _{\infty }\) and \(|\varphi (0)|\).
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Fatehi, M., Hammond, C.N.B. Norms of Weighted Composition Operators with Automorphic Symbol. Integr. Equ. Oper. Theory 92, 13 (2020). https://doi.org/10.1007/s00020-020-2570-y
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DOI: https://doi.org/10.1007/s00020-020-2570-y