Closures of Bergman–Besov Spaces in the Weighted Bloch Spaces on the Unit Ball

2021 ◽  
Vol 15 (6) ◽  
Author(s):  
Nihat Gökhan Göğüş ◽  
Faruk Yilmaz
Keyword(s):  
Unit Ball ◽  
Besov Spaces ◽  
Bloch Spaces

Riemann-Stieltjes operators between α -Bloch spaces and Besov spaces

2009 ◽  
Vol 282 (6) ◽  
pp. 899-911 ◽  
Author(s):  
Songxiao Li ◽  
Stevo Stević
Keyword(s):  
Besov Spaces ◽  
Bloch Spaces

scholarly journals The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Xi Fu ◽  
Zhiyao Xu ◽  
Xiaoyou Liu
Keyword(s):  
Unit Ball ◽  
Besov Spaces ◽  
Multi Index ◽  
The Real

LetBbe the real unit ball inRnandf∈CN(B). Given a multi-indexm=(m1,…,mn)of nonnegative integers with|m|=N, we set the quantitysupx∈B,y∈E(x,r),x≠y(1-|x|2)α(1-|y|2)β|∂mf(x)-∂mf(y)|/|x-y|γ[x,y]1-γ,  x≠y,where0≤γ≤1andα+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.

scholarly journals Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

2009 ◽  
Vol 7 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Ze-Hua Zhou ◽  
Min Zhu
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Besov Spaces ◽  
Complex Space ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Cesàro Operator ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Cesaro Operator

Let 𝑔 be a holomorphic of the unit ballBin then-dimensional complex space, and denote byTgthe extended Cesáro operator with symbolg. Let 0 <p< +∞, −n− 1 <q< +∞,q> −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness ofTgbetween generalized Besov spaceB(p, q)and 𝛼α- Bloch spaceℬαin the unit ball, and also present some necessary and sufficient conditions.

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 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
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