Musielak–Orlicz BMO-type Spaces Associated with Generalized Approximations to the Identity

Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2014-11, Vol.30 (11), p.1917-1962
Main Authors: Hou, Shao Xiong, Yang, Da Chun, Yang, Si Bei
Format: Article
Language:English
Subjects:
Approximation
BMO
Equivalence
Euclidean space
Functions (mathematics)
Group theory
Inequalities
Laplace transforms
Mathematical analysis
Mathematical functions
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Orlicz函数
Poisson distribution
Studies
Texts
Theorems
广义
拉普拉斯算子
空间
等价刻画
逼近
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Summary:Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-014-3181-9