Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space

Eungil Ko, Ji Eun Lee, Jongrak Lee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we propose the generalized derivative Hardy space Sα,β2(D) which consists of functions whose derivatives are in the Hardy and Bergman spaces. In particular, we state basic results for Sα,β2(D) and focus on m-isometric multiplication operators. Moreover, we consider the complete Pick property in Sα,β2(D) and several applications of having the complete Pick property, which is related to the multiplication operators and composition operators. Finally, we study the Toeplitz operators on Sα,β2(D) and investigate a necessary and sufficient condition for the hyponormality of Toeplitz operator Tφ on Sα,β2(D).

Original languageEnglish
Pages (from-to)4143-4164
Number of pages22
JournalComplex Analysis and Operator Theory
Volume13
Issue number8
DOIs
StatePublished - 1 Nov 2019

Keywords

  • Complete Pick property
  • Derivative Hardy spaces
  • Hyponormal
  • m-isometry
  • Multiplication operator
  • Toepltiz operator

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