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.

العنوان

J. Results Math

الناشر

Springer International Publishing

بلد الناشر

سويسرا

Indexing

Thomson Reuters

معامل التأثير

0,969

نوع المنشور

مطبوع فقط

المجلد

75

السنة

2019

الصفحات

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