Composition operator on finite type model domains and certain weighted Bergman spaces over the unit ball.

Hyungwoon Koo; Song Ying Li

Composition operator on finite type model domains and certain weighted Bergman spaces over the unit ball.

Department of Mathematics

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

Abstract

We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.

Original language	English
Pages (from-to)	87-114
Number of pages	28
Journal	Houston Journal of Mathematics
Volume	45
Issue number	1
Publication status	Published - 2019

Keywords

Boundedness
Composition operator
Finite type domain
Smooth symbol

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "Composition operator on finite type model domains and certain weighted Bergman spaces over the unit ball.",

abstract = "We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.",

keywords = "Boundedness, Composition operator, Finite type domain, Smooth symbol",

author = "Hyungwoon Koo and Li, {Song Ying}",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 47B33; Secondary 32A36, 32T25. Key words and phrases. Composition operator, finite type domain, boundedness, smooth symbol. H. Koo was supported by NRF of Korea(2017R1A2B20025). Funding Information: H. Koo was supported by NRF of Korea(2017R1A2B20025). Part of this research was performed during the first author{\textquoteright}s visit to University of California at Irvine. He thanks the Mathematics Department of University of California at Irvine for its hospitality and support. Publisher Copyright: {\textcopyright} 2019 University of Houston.",

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N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 47B33; Secondary 32A36, 32T25. Key words and phrases. Composition operator, finite type domain, boundedness, smooth symbol. H. Koo was supported by NRF of Korea(2017R1A2B20025). Funding Information: H. Koo was supported by NRF of Korea(2017R1A2B20025). Part of this research was performed during the first author’s visit to University of California at Irvine. He thanks the Mathematics Department of University of California at Irvine for its hospitality and support. Publisher Copyright: © 2019 University of Houston.

PY - 2019

Y1 - 2019

N2 - We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.

AB - We give a characterization for the boundedness of a composition operator on the Bergman space over the two dimensional finite type model domains. For which, we study the boundedness of the composition operators on some singular weighted Bergman space over the two dimensional unit ball. We investigate composition operators on these singular weighted Bergman spaces over the unit ball with smooth symbols, and provide various interesting examples which reveal quite different phenomena from those on the usual weighted Bergman spaces over the unit ball.

KW - Boundedness

KW - Composition operator

KW - Finite type domain

KW - Smooth symbol

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JO - Houston Journal of Mathematics

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Composition operator on finite type model domains and certain weighted Bergman spaces over the unit ball.

Abstract

Keywords

ASJC Scopus subject areas

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