Carleson measure characterization of Bloch functions

1996 ◽  
Vol 12 (2) ◽  
pp. 175-184 ◽  
Author(s):  
Lou Zengjian
Keyword(s):  
Carleson Measure ◽  
Bloch Functions

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

A Real Characterization of the Pre-Dual of Bloch Functions

1983 ◽  
Vol s2-27 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Geraldo Soares de Souza ◽  
G. Sampson
Keyword(s):  
Bloch Functions

scholarly journals A CHARACTERIZATION OF BLOCH FUNCTIONS

2006 ◽  
Vol 21 (2) ◽  
pp. 287-292 ◽  
Author(s):  
Ern-Gun Kwon ◽  
Ok-Hee Shim ◽  
Eun-Kyu Bae
Keyword(s):  
Bloch Functions

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).

ON THE HOLLAND–WALSH CHARACTERIZATION OF BLOCH FUNCTIONS

2008 ◽  
Vol 51 (2) ◽  
pp. 439-441 ◽  
Author(s):  
Miroslav Pavlović
Keyword(s):  
Unit Ball ◽  
Bloch Functions

AbstractIt is proved that the Bloch norm of an arbitrary $C^1$-function defined on the unit ball $\mathbb{B}_n\subset\mathbb{R}^n$ is equal to$$ \sup_{x,y\in\mathbb{B}_n,\,x\neq y}{(1-|x|^2)^{1/2}(1-|y|^2)^{1/2}}\frac{|f(x)-f(y)|}{|x-y|}. $$

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.

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