scholarly journals Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball

2018 ◽  
Vol 69 (2) ◽  
pp. 503-523 ◽  
Author(s):  
Ömer Faruk Doğan ◽  
Adem Ersin Üreyen
Keyword(s):  
Unit Ball ◽  
Bloch Spaces ◽  
Inclusion Relations

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.

On Classes for Hyperbolic Riemann Surfaces

2016 ◽  
Vol 59 (01) ◽  
pp. 13-29
Author(s):  
Rauno Aulaskari ◽  
Huaihui Chen
Keyword(s):  
Unit Ball ◽  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Inclusion Relations ◽  
Hyperbolic Riemann Surfaces ◽  
Qp Spaces

AbstractThe Qpspaces of holomorphic functions on the disk, hyperbolic Riemann surfaces or complex unit ball have been studied deeply. Meanwhile, there are a lot of papers devoted to theclasses of meromorphic functions on the disk or hyperbolic Riemann surfaces. In this paper, we prove the nesting property (inclusion relations) ofclasses on hyperbolic Riemann surfaces. The same property for Qp spaces was also established systematically and precisely in earlier work by the authors of this paper.

scholarly journals Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

2009 ◽  
Vol 7 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

Sign in / Sign up

Export Citation Format

Share Document