COMPOSITION OPERATORS BETWEEN μ-BLOCH SPACES ON CARTAN-HARTOGS DOMAIN OF THE FIRST TYPE

2020 ◽  
Vol 126 (1) ◽  
pp. 65-88
Author(s):  
Ziyi Zhang
Keyword(s):  
Composition Operators ◽  
Bloch Spaces ◽  
Hartogs Domain

scholarly journals Composition Operators from p-Bloch Space to q-Bloch Space on the Fourth Cartan-Hartogs Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Jianbing Su ◽  
Chao Zhang
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Bloch Spaces ◽  
Hartogs Domain ◽  
Hartogs Domains

We obtain new generalized Hua’s inequality corresponding to YIV(N,n;K), where YIV(N,n;K) denotes the fourth Cartan-Hartogs domain in CN+n. Furthermore, we introduce the weighted Bloch spaces on YIV(N,n;K) and apply our inequality to study the boundedness and compactness of composition operator Cϕ from βp(YIV(N,n;K)) to βq(YIV(N,n;K)) for p≥0 and q≥0.

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

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