scholarly journals Harmonic Besov Spaces on the Unit Ball in ${\bf R}^n$

2001 ◽  
Vol 31 (4) ◽  
pp. 1305-1316 ◽  
Author(s):  
Miroljub Jevtić ◽  
Miroslav Pavlović
Keyword(s):  
Unit Ball ◽  
Besov 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.

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 Maximal and Area Integral Characterizations of Bergman Spaces in the Unit Ball ofℂn

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Zeqian Chen ◽  
Wei Ouyang
Keyword(s):  
Unit Ball ◽  
Besov Spaces ◽  
Atomic Decomposition ◽  
Bergman Spaces ◽  
Real Variable ◽  
Maximal Functions ◽  
Radial Derivative ◽  
Area Integral ◽  
Variable Type ◽  
Complex Gradient

We present maximal and area integral characterizations of Bergman spaces in the unit ball ofℂn. The characterizations are in terms of maximal functions and area integral functions on Bergman balls involving the radial derivative, the complex gradient, and the invariant gradient. As an application, we obtain new maximal and area integral characterizations of Besov spaces. Moreover, we give an atomic decomposition of real-variable type with respect to Carleson tubes for Bergman spaces.

scholarly journals Schatten-von Neumann properties of bilinear Hankel forms of higher weights

2006 ◽  
Vol 98 (2) ◽  
pp. 283
Author(s):  
Marcus Sundhäll
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Besov Spaces ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Von Neumann ◽  
Higher Weights ◽  
Vector Valued

Hankel forms of higher weights, on weighted Bergman spaces in the unit ball of $\mathsf{C}^d$, were introduced by Peetre. Each Hankel form corresponds to a vector-valued holomorphic function, called the symbol of the form. In this paper we characterize bounded, compact and Schatten-von Neumann $\mathcal{S}_p$ class ($2\leq p<\infty$) Hankel forms in terms of the membership of the symbols in certain Besov spaces.

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