Joint Carleson measure and the difference of composition operators on Aα p(Bn)

Hyung Woon Koo, Maofa Wang

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15 Citations (Scopus)

Abstract

We introduce a concept of joint Carleson measure and characterize when the difference of two composition operators on Aα p(Bn), the weighted Bergman space over the unit ball Bn in Cn, is bounded or compact. We apply this joint Carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n ≥ 2. This is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p>0. Moreover, the compact difference on the weighted Bergman spaces over the unit disc is known to be independent of p>0, and the compact difference on Aα p(Bn) is known to be independent of p>0 if each composition operator is bounded on Aβ p(Bn) for some -1< β < α [2].

Original languageEnglish
Pages (from-to)1119-1142
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Volume419
Issue number2
DOIs
Publication statusPublished - 2014 Nov 15

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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