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 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 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 Landau’s theorem for slice regular functions on the quaternionic unit ball

2017 ◽  
Vol 28 (03) ◽  
pp. 1750017 ◽  
Author(s):  
Cinzia Bisi ◽  
Caterina Stoppato
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Analogous Result ◽  
Open Unit ◽  
Open Unit Ball ◽  
Slice Regular Functions ◽  
New Approach ◽  
The Real ◽  
Regular Functions ◽  
Real Algebra

During the development of the theory of slice regular functions over the real algebra of quaternions [Formula: see text] in the last decade, some natural questions arose about slice regular functions on the open unit ball [Formula: see text] in [Formula: see text]. This work establishes several new results in this context. Along with some useful estimates for slice regular self-maps of [Formula: see text] fixing the origin, it establishes two variants of the quaternionic Schwarz–Pick lemma, specialized to maps [Formula: see text] that are not injective. These results allow a full generalization to quaternions of two theorems proven by Landau for holomorphic self-maps [Formula: see text] of the complex unit disk with [Formula: see text]. Landau had computed, in terms of [Formula: see text], a radius [Formula: see text] such that [Formula: see text] is injective at least in the disk [Formula: see text] and such that the inclusion [Formula: see text] holds. The analogous result proven here for slice regular functions [Formula: see text] allows a new approach to the study of Bloch–Landau-type properties of slice regular functions [Formula: see text].

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