Linear Combinations of Composition Operators on the Fock-Sobolev Spaces

Research output: Contribution to journalArticle

15 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
JournalPotential Analysis
DOIs
Publication statusAccepted/In press - 2014 Jun 7

Fingerprint

Fock Space
Composition Operator
Sobolev Spaces
Linear Combination
Schatten Class
Compactness
Several Variables
Cancellation
Function Space
Unit Disk
Analogue
Operator

ASJC Scopus subject areas

  • Analysis

Cite this

Linear Combinations of Composition Operators on the Fock-Sobolev Spaces. / Cho, Hong Rae; Choe, Boo Rim; Koo, Hyung Woon.

In: Potential Analysis, 07.06.2014.

Research output: Contribution to journalArticle

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