A note on composition operators acting on holomorphic sobolev spaces

Research output: Contribution to journalArticle

Abstract

A holomorphic self-map φ of the unit disk is constructed such that the composition operator induced by φ is bounded on the Hardy-Sobolev space H1/2 of order 2 as well as on the ordinary holomorphic Lipschitz space Lip1 but unbounded on the Zygmund class Λ1. Among these three function spaces we have embedding relations H1/2 ⊂ Lip1 ⊂ Λ1. So, the main points here are that our construction provides a composition operator which is bounded on smaller spaces, but not on a larger space and that all the function spaces involved are standard ones.

Original languageEnglish
Pages (from-to)4369-4375
Number of pages7
JournalProceedings of the American Mathematical Society
Volume139
Issue number12
DOIs
Publication statusPublished - 2011 Dec

Keywords

  • Composition operator
  • Holomorphic sobolev spaces
  • Zygmund class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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