scholarly journals Characterizations of Bloch space and Besov spaces by oscillations

2000 ◽  
Vol 29 (2) ◽  
pp. 409-451 ◽  
Author(s):  
Rikio YONEDA
Keyword(s):  
Besov Spaces ◽  
Bloch Space

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.

scholarly journals The Bloch space and Besov spaces of analytic functions

1996 ◽  
Vol 54 (2) ◽  
pp. 211-219 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Elementary Proof ◽  
Bloch Space ◽  
Little Bloch Space ◽  
Spaces Of Analytic Functions

We shall give an elementary proof of a characterisation for the Bloch space due to Holland and Walsh, and obtain analogous characterisations for the little Bloch space and Besov spaces of analytic functions on the unit disk in the complex plane.

scholarly journals WEIGHTED LIPSCHITZ CONTINUITY AND HARMONIC BLOCH AND BESOV SPACES IN THE REAL UNIT BALL

2005 ◽  
Vol 48 (3) ◽  
pp. 743-755 ◽  
Author(s):  
Guangbin Ren ◽  
Uwe Kähler
Keyword(s):  
Unit Ball ◽  
Besov Spaces ◽  
Lipschitz Continuity ◽  
Bloch Space ◽  
The Real

AbstractThe characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of $\mathbb{R}^n$. Similar results are obtained for little Bloch and Besov spaces.

scholarly journals Distances from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂn

2009 ◽  
Vol 7 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Wen Xu
Keyword(s):  
Unit Ball ◽  
Besov Spaces ◽  
Bloch Space ◽  
Invariant Function ◽  
Function Spaces ◽  
Bloch Functions ◽  
Distance Formulae ◽  
Little Bloch Space

Distance formulae from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂnsuch asQsspaces, little Bloch spaceℬ0and Besov spacesBpare given.

scholarly journals Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Composition Operator ◽  
Besov Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition ◽  
Special Case

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.

A NEW ESSENTIAL NORM ESTIMATE OF COMPOSITION OPERATORS FROM α-BLOCH SPACES INTO μ-BLOCH SPACES

2013 ◽  
Vol 24 (14) ◽  
pp. 1350104 ◽  
Author(s):  
JULIO C. RAMOS-FERNÁNDEZ
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Besov Spaces ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate

Let μ be any weight function defined on the unit disk 𝔻 and let ϕ be an analytic self-map of 𝔻. In this paper, we show that the essential norm of composition operator Cϕ mapping from the α-Bloch space, with α > 0, to μ-Bloch space [Formula: see text] is comparable to [Formula: see text] where, for a ∈ 𝔻, σa is a certain special function in α-Bloch space. As a consequence of our estimate, we extend recent results, about the compactness of composition operators, due to Tjani in [Compact composition operators on Besov spaces, Trans. Amer. Math. Soc.355(11) (2003) 4683–4698] and Malavé Ramírez and Ramos-Fernández in [On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces, C. R. Math. Acad. Sci. Paris351 (2013) 23–26, http://dx.doi.org/10.1016/j.crma.2012.11.013 ].

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