Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
By M. Jury. 2007
49 citations recorded by the source corpus.
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 as- sociated 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. Sim- ilar 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 functions spaces on the unit ball.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4f30ab1da381cf15bbc4dfe8fa8c2b4fc5cc3888
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Composition operators on Hardy spaces of a half‐plane (2009, methodology): “However, as noted in [8] (in the case of the disc), if this operator is bounded, then for its (unique) bounded extension to H(2) (still denoted by C∗ φ) we have 〈(C∗ φ)f, kw〉 = 〈f, C∗ φkw〉 = f(φ(w)), (3.”