TY - JOUR
T1 - Multiplication and Toeplitz Operators on the Generalized Derivative Hardy Space
AU - Ko, Eungil
AU - Lee, Ji Eun
AU - Lee, Jongrak
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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).
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).
KW - Complete Pick property
KW - Derivative Hardy spaces
KW - Hyponormal
KW - m-isometry
KW - Multiplication operator
KW - Toepltiz operator
UR - http://www.scopus.com/inward/record.url?scp=85073973843&partnerID=8YFLogxK
U2 - 10.1007/s11785-019-00954-7
DO - 10.1007/s11785-019-00954-7
M3 - Article
AN - SCOPUS:85073973843
SN - 1661-8254
VL - 13
SP - 4143
EP - 4164
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 8
ER -