Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

Abstract : It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \leq p < \infty$, is also compact on the Bergman space ${\mathfrak B}^p = L^p_a (\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^\Psi$ and Bergman-Orlicz ${\mathfrak B}^\Psi$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^\Psi$ but not on ${\mathfrak B}^\Psi$.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download
Contributor : Daniel Li Connect in order to contact the contributor
Submitted on : Monday, March 21, 2011 - 10:43:40 AM
Last modification on : Friday, January 21, 2022 - 3:30:41 AM
Long-term archiving on: : Wednesday, June 22, 2011 - 9:53:28 AM


Files produced by the author(s)


  • HAL Id : hal-00530387, version 2
  • ARXIV : 1010.6207



Daniel Li. Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces. {date}. ⟨hal-00530387v2⟩



Record views


Files downloads