Open AccessОграниченные композиционные операторы на весовых функциональных пространствах на единичном круге
Author(s) -
Sheng Hao Hua,
L.H. Khoi,
P.T. Tien
Publication year - 2020
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/p4238-0191-2122-t
Subject(s) - mathematics , hardy space , holomorphic function , bounded function , space (punctuation) , unit disk , bergman space , pure mathematics , operator (biology) , composition (language) , beta (programming language) , monomial , combinatorics , mathematical analysis , philosophy , linguistics , biochemistry , chemistry , repressor , computer science , transcription factor , gene , programming language
We introduce a general class of weighted spaces $\calH(\beta)$ of holomorphic functions in the unit disk $\mathbb{D}$, which contains several classical spaces, such as Hardy space, Bergman space, Dirichlet space. We~characterize boundedness of composition operators $C_{\varphi}$ induced by affine and monomial symbols $\varphi$ on these spaces $\calH(\beta)$. We also establish a sufficient condition under which the operator $C_{\varphi}$ induced by the symbol $\varphi$ with relatively compact image $\varphi(\mathbb{D})$ in $\mathbb{D}$ is bounded on $\calH(\beta)$. Note that in the setting of $\calH(\beta)$, the characterizations of boundedness of composition operators $C_{\varphi}$ depend closely not only on functional properties of the symbols $\varphi$ but also on the behavior of the weight sequence $\beta$.