Boundedness from below of composition operators on the Bloch spaces

2003 ◽  
Vol 46 (6) ◽  
pp. 838 ◽  
Author(s):  
Huaihui CHEN
Keyword(s):  
Composition Operators ◽  
Bloch Spaces

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.

scholarly journals Linear Combinations of Composition Operators on the Bloch Spaces

2011 ◽  
Vol 63 (4) ◽  
pp. 862-877 ◽  
Author(s):  
Takuya Hosokawa ◽  
Pekka J. Nieminen ◽  
Shûichi Ohno
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Linear Combinations ◽  
Bloch Spaces ◽  
Little Bloch Space

Abstract We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space.

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