非双倍测度Marcinkiewicz积分交换子和多线性交换子的弱型估计(英文）  

Weak Type Estimates for Commutators and Multilinear Commutators of Marcinkiewicz Integrals With Non-doubling Measures

作　　者：卢盛栋 江寅生[1] 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐新疆830046

出　　处：《数学进展》2014年第1期103-117,共15页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.10861010,No.11161044);Xinjiang Province Natural Science Foundation of China(No.2011211A005)

摘　　要：设μ为R^d上的非负Radon测度,仅满足增长条件:对所有的x∈R^d,r>0有μ(B(x,r))≦C_0r^n,其中C_0是一个固定的常数且0<n≤d.在非双倍测度下,本文建立了Marcinkiewicz积分与Orlicz型函数生成的交换子和多线性交换子从L(logL)^(1/r)(μ)到弱L^1(μ)的有界性.Let # be a nonnegative Radon measure on Rd which only satisfies the growth condition μ（B（x,r）） ≤ Cor^n for all x ∈Rd and r 〉 0, where Co is a fixed constant and （μ） to 0 〈 n 〈 d. The purpose of this paper is to establish the boundedness from L（log 1 weak Li-（#） for the commutators and the multilinear commutators generated by Marcinkiewicz integrals and Orlicz type functions with the non-doubling measures #.

关 键 词：MARCINKIEWICZ积分 Orlicz型函数 交换子 多线性交换子 非双倍测度 

分 类 号：O174.2[理学—数学]