Joint Carleson measure for the difference of composition operators on the polydisks

Hyungwoon Koo, Inyoung Park, Maofa Wang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In Koo and Wang (Joint Carleson measure and the difference of composition operators on (Formula presented.). J Math Anal Appl. 2014;419:1119–1142), the authors introduced a concept of joint Carleson measure and used it to characterize when the difference of two composition operators on weighted Bergman space over the unit ball is bounded or compact. In this paper, we extend the concept of joint Carleson measure to the polydisk setting and obtain analogue characterizations of the boundedness (compactness, resp.) of the difference of two composition operators on the weighted Bergman spaces over the unit polydisk, which may provide a unified approach for various ad hoc studies on the boundedness or the compactness of the difference of composition operators on polydisk. Moreover, we construct a concrete example to show that both the boundedness and the compactness depend on the index p when the dimension (Formula presented.), which is in sharp contrast with the one-variable case where the boundedness and the compactness of the difference of two composition operators are independent of p>0. Due to the complexity of the Carleson measure on the unit polydisk, some new techniques are required in the polydisk setting.

Original languageEnglish
Pages (from-to)1352-1378
Number of pages27
JournalComplex Variables and Elliptic Equations
Volume67
Issue number6
DOIs
Publication statusPublished - 2022

Bibliographical note

Funding Information:
H. Koo was supported by NRF (2017R1A2B2002515) of Korea and NSFC (11771340), M. Wang was supported by NSFC (11771340) and I. Park was supported by NRF (2018R1D1A1B07046890) of Korea. Part of this research was performed during the third author's visit to Korea University. He thanks the mathematics department of Korea University for their hospitality and support. The authors thank the dedicated referee who provided numerous valuable comments that improved the overall presentation of the paper, especially the proof of the necessity of our main result, and informed us the relevant reference [8 ].

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • Difference of composition operators
  • boundedness
  • compactness
  • joint Carleson measure
  • weighted bergman space

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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