On the Carleson Measure Characterization of BMOA Functions on the Unit Ball

1992 ◽  
Vol 114 (2) ◽  
pp. 379 ◽  
Author(s):  
Miroljub Jevtic
Keyword(s):  
Unit Ball ◽  
Carleson Measure

scholarly journals Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Stéphane Charpentier ◽  
Benoît Sehba
Keyword(s):  
Unit Ball ◽  
Orlicz Space ◽  
Carleson Measure ◽  
Composition Operators ◽  
Orlicz Spaces ◽  
Growth Functions

We characterize those measuresμfor which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) spaceHΨ1(resp.,AαΨ1) of the unit ball ofCNembeds boundedly or compactly into the Orlicz spaceLΨ2(BN¯,μ)(resp.,LΨ2(BN,μ)), when the defining functionsΨ1andΨ2are growth functions such thatL1⊂LΨjforj∈{1,2}, and such thatΨ2/Ψ1is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators fromHΨ1(resp.,AαΨ1) intoHΨ2(resp.,AαΨ2).

A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

2012 ◽  
Vol 55 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Songxiao Li ◽  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

scholarly journals A CHARACTERIZATION OF WEIGHTED BERGMAN-PRIVALOV SPACES ON THE UNIT BALL OF Cn

2002 ◽  
Vol 39 (5) ◽  
pp. 783-800 ◽  
Author(s):  
Yasuo Matsugu ◽  
Jun Miyazawa ◽  
Sei-Ichiro Ueki
Keyword(s):  
Unit Ball

scholarly journals Complex extreme measurable selections

1995 ◽  
Vol 58 (2) ◽  
pp. 222-231
Author(s):  
Douglas Mupasiri
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Point ◽  
Measure Space ◽  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Closed Unit Ball ◽  
Measurable Selections ◽  
Necessary And Sufficient

AbstractWe give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.

scholarly journals Geometry of multilinear forms

2019 ◽  
Vol 22 (02) ◽  
pp. 1950011 ◽  
Author(s):  
W. V. Cavalcante ◽  
D. M. Pellegrino ◽  
E. V. Teixeira
Keyword(s):  
Unit Ball ◽  
Extreme Points ◽  
Linear Forms ◽  
Multilinear Forms ◽  
Elementary Steps ◽  
Full Characterization ◽  
Constructive Process

We develop a constructive process which determines all extreme points of the unit ball in the space of [Formula: see text]-linear forms, [Formula: see text] Our method provides a full characterization of the geometry of that space through finitely many elementary steps, and thus it can be extensively applied in both computational as well as theoretical problems; few consequences are also derived in this paper.

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