We study the compactness of the composition operator on de Branges–Rovnyak spaces. Inspired by a paper by Lyubarskii–Malinnikova on model spaces, we give some necessary and some sufficient conditions for compactness. In the paper of Lyubarskii-Malinnikova, the key point is some Bernstein inequality on model spaces due to Cohn (and based on a deep inequality of Axler–Chang–Sarason involving the Hardy–Littlewood maximal function). We generalize the result of Cohn to some subspace of a de Branges–Rovnyak space (in many cases dense) and then get a sufficient condition (analogue to Lyubarskii–Malinnikova’s condition) for compactness of the composition operator on that subspace.

Title

J. Results Math

Publisher

Springer International Publishing

Publisher Country

Switzerland

Indexing

Thomson Reuters

Impact Factor

0.969

Publication Type

Prtinted only

Volume

75

Year

2019

Pages

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