Linear combinations of composition operators on the fock-sobolev spaces

Hong Rae Cho; Boo Rim Choe; Hyungwoon Koo

doi:10.1007/s11118-014-9417-6

Linear combinations of composition operators on the fock-sobolev spaces

Hong Rae Cho, Boo Rim Choe, Hyungwoon Koo

Research output: Contribution to journal › Article › peer-review

38 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 language	English
Pages (from-to)	1223-1246
Number of pages	24
Journal	Potential Analysis
Volume	41
Issue number	4
DOIs	https://doi.org/10.1007/s11118-014-9417-6
Publication status	Published - 2014 Oct 11

Bibliographical note

Funding Information:
H. Cho was supported by NRF of Korea (2011-0013740), B. Choe was supported by NRF of Korea (2013R1A1A2004736) and H. Koo was supported by NRF of Korea(2012R1A1A2000705) and NSFC (11271293).

Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.

Keywords

Fock space
Fock-sobolev space
Linear combination of composition operators

ASJC Scopus subject areas

Analysis

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10.1007/s11118-014-9417-6

Cite this

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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.",

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N2 - 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.

AB - 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.

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Linear combinations of composition operators on the fock-sobolev spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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