Composition operators acting on holomorphic Sobolev spaces

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12 Citations (Scopus)


We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

Original languageEnglish
Pages (from-to)2829-2855
Number of pages27
JournalTransactions of the American Mathematical Society
Issue number7
Publication statusPublished - 2003 Jul


  • Bergman space
  • Composition operator
  • Fractional derivative

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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