Characterization of BMO p sq - functions by generalized Carleson measure

1991 ◽  
pp. 84-94
Author(s):  
Chun Li
Keyword(s):  
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).

Two-Weight Norm Inequality and Carleson Measure in Weighted Hardy Spaces

1992 ◽  
Vol 44 (6) ◽  
pp. 1206-1219 ◽  
Author(s):  
Dangsheng Gu
Keyword(s):  
Homogeneous Space ◽  
Hardy Spaces ◽  
Maximal Operator ◽  
Carleson Measure ◽  
Norm Inequality ◽  
Doubling Measure ◽  
Weight Norm Inequality ◽  
Weighted Hardy Spaces

AbstractLet (X, ν, d) be a homogeneous space and let Ω be a doubling measure on X. We study the characterization of measures μ on X+ = X x R+ such that the inequality , where q < p, holds for the maximal operator Hvf studied by Hörmander. The solution utilizes the concept of the “balayée” of the measure μ.

scholarly journals A Characterization of Weighted Carleson Measure Spaces

2019 ◽  
Vol 23 (1) ◽  
pp. 103-127
Author(s):  
Hsun-Wu Liu ◽  
Kunchuan Wang
Keyword(s):  
Carleson Measure ◽  
Measure Spaces

scholarly journals LUSIN AREA FUNCTION AND MOLECULAR CHARACTERIZATIONS OF MUSIELAK–ORLICZ HARDY SPACES AND THEIR APPLICATIONS

2013 ◽  
Vol 15 (06) ◽  
pp. 1350029 ◽  
Author(s):  
SHAOXIONG HOU ◽  
DACHUN YANG ◽  
SIBEI YANG
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Carleson Measure ◽  
Dual Space ◽  
Growth Function ◽  
Area Function ◽  
Type Space ◽  
Lusin Area Function

Let φ : ℝn× [0,∞) → [0,∞) be a growth function such that φ(x, ⋅) is nondecreasing, φ(x, 0) = 0, φ(x, t) > 0 when t > 0, limt→∞φ(x, t) = ∞, and φ(⋅, t) is a Muckenhoupt A∞(ℝn) weight uniformly in t. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak–Orlicz Hardy space Hφ(ℝn) introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the φ-Carleson measure characterization of the Musielak–Orlicz BMO-type space BMOφ(ℝn), which was proved to be the dual space of Hφ(ℝn) by Luong Dang Ky.

Carleson Measure Characterization of Weighted BMO Associated with a Family of General Sets

2016 ◽  
Vol 27 (1) ◽  
pp. 842-867 ◽  
Author(s):  
Yong Ding ◽  
Ming-Yi Lee ◽  
Chin-Cheng Lin
Keyword(s):  
Carleson Measure ◽  
Weighted Bmo

CARLESON MEASURE SPACES ASSOCIATED TO PARA-ACCRETIVE FUNCTIONS

2012 ◽  
Vol 14 (01) ◽  
pp. 1250002 ◽  
Author(s):  
MING-YI LEE ◽  
CHIN-CHENG LIN
Keyword(s):  
Hardy Spaces ◽  
Carleson Measure ◽  
Dual Space ◽  
Cauchy Integrals ◽  
Measure Spaces

To study the boundedness of the Cauchy integrals over Lipschitz curves, new Hardy spaces [Formula: see text] were introduced in [Y. Han, M.-Y. Lee and C.-C. Lin, Hardy spaces and the Tb theorem, J. Geom. Anal.14 (2004) 291–318], where b is a para-accretive function. In this paper, we define the Carleson measure spaces [Formula: see text] that generalize BMO, and show that [Formula: see text] is the dual space of [Formula: see text]. As an application, we give a Carleson measure characterization of BMOb.

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