Composition operators on Hardy-Orlicz spaces

By Pascal Lefèvre, Daniel Li, Hervé Queffélec, L. Rodríguez-Piazza. 2006

66 citations recorded by the source corpus.

We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Ψ grows rapidly: compactness, weak compactness, to be psumming, order bounded, . . . , and show how these notions behave according to the growth of Ψ. We introduce an adapted version of Carleson measure. We construct various examples showing that our results are essentially sharp. In the last part, we study the case of Bergman-Orlicz spaces. Mathematics Subject Classification. Primary: 47 B 33 – 46 E 30; Secondary: Key-words. Bergman-Orlicz space – Carleson measure – composition operator – Hardy-Orlicz space

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30ee94071dc67a2ef3d6c3be4d7d6820edb07044