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Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space
- Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space
- Ko, Eungil; Lee, Ji Eun; Lee, Jongrak
- Ewha Authors
- 고응일; 이종락
- SCOPUS Author ID
- Issue Date
- Journal Title
- COMPLEX ANALYSIS AND OPERATOR THEORY
- COMPLEX ANALYSIS AND OPERATOR THEORY vol. 13, no. 8, pp. 4143 - 4164
- Derivative Hardy spaces; Multiplication operator; m-isometry; Complete Pick property; Toepltiz operator; Hyponormal
- SPRINGER BASEL AG
- SCIE; SCOPUS
- Document Type
- In this paper, we propose the generalized derivative Hardy space S-alpha,beta(2)(D) which consists of functions whose derivatives are in the Hardy and Bergman spaces. In particular, we state basic results for S-alpha,beta(2) (D) and focus on m-isometric multiplication operators. Moreover, we consider the complete Pick property in S-alpha,beta(2)(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 S-alpha,beta(2)(D) and investigate a necessary and sufficient condition for the hyponormality of Toeplitz operator T-phi on S-alpha,beta(2)(D).
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