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

作　　者：Shao Xiong HOU Da Chun YANG Si Bei YANG 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education [2]School of Mathematics and Statistics,Lanzhou University

出　　处：《Acta Mathematica Sinica,English Series》2014年第11期1917-1962,共46页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171027 and 11361020);the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003);the Fundamental Research Funds for Central Universities of China(Grant Nos.2012LYB26,2012CXQT09 and lzujbky-2014-18)

摘　　要：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.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.

关 键 词：Growth function BMO-type space approximation to the identity John–Nirenberg inequality Carleson measure 

分 类 号：O177[理学—数学]