Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space

Eungil Ko; Ji Eun Lee; Jongrak Lee

doi:10.1007/s11785-019-00954-7

Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space

Eungil Ko, Ji Eun Lee, Jongrak Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 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 T_φ on Sα,β2(D).

Original language	English
Pages (from-to)	4143-4164
Number of pages	22
Journal	Complex Analysis and Operator Theory
Volume	13
Issue number	8
DOIs	https://doi.org/10.1007/s11785-019-00954-7
State	Published - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

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

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10.1007/s11785-019-00954-7

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AB - 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).

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Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space

Abstract

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Keywords

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