Endpoint Estimates of Generalized Homogeneous Littlewood–Paley g-functions over Non-Homogeneous Metric Measure Spaces  

作　　者：Xing FU Ji Man ZHAO 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2016年第9期1035-1074,共40页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11471040);the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)

摘　　要：Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.

关 键 词：Non-homogeneous metric measure space generalized homogeneous Littlewood-Paley g-function Hardy space RBMO（u） RBLO（u） vector valued Calderon Zygmund theory 

分 类 号：O177[理学—数学]