Composition Operators on Hardy-Orlicz Spaces

by Pascal Lefevre, Daniel Li, Hervé Queffelec

The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Psi grows compactness, weak compactness, to be p-summing, order bounded, ldots, and show how these notions behave according to the growth of Psi. They introduce an adapted version of Carleson measure. They construct various examples showing that their results are essentially sharp. In the last part, they study the case of Bergman-Orlicz spaces.

74 pages, Paperback

First published September 15, 2010