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• W2062601049 abstract "We prove that the norm of a weighted composition operator on the Hardy space $H^2$ of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on $H^2$ and recover the standard upper bound for the norm. Similar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard function spaces on the unit ball." @default.
• W2062601049 created "2016-06-24" @default.
• W2062601049 creator A5029999741 @default.
• W2062601049 date "2007-11-01" @default.
• W2062601049 modified "2023-10-12" @default.
• W2062601049 title "Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators" @default.
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• W2062601049 doi "https://doi.org/10.1090/s0002-9939-07-08931-9" @default.
• W2062601049 hasPublicationYear "2007" @default.
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