Linear combinations of composition operators on the fock-sobolev spaces

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23 Citations (Scopus)

Abstract

We study linear combinations of composition operators acting on the Fock-Sobolev spaces of several variables. We show that such an operator is bounded only when all the composition operators in the combination are bounded individually. In other words, composition operators on the Fock-Sobolev spaces do not possess the same cancelation properties as composition operators on other well-known function spaces over the unit disk. We also show the analogues for compactness and the membership in the Schatten classes. In particular, compactness and the membership in some/all of the Schatten classes turn out to be the same.

Original languageEnglish
Pages (from-to)1223-1246
Number of pages24
JournalPotential Analysis
Volume41
Issue number4
DOIs
Publication statusPublished - 2014 Oct 11

Keywords

  • Fock space
  • Fock-sobolev space
  • Linear combination of composition operators

ASJC Scopus subject areas

  • Analysis

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