具有广义核的多线性平方算子与交换子的加权估计  

Weighted Estimates for Some Multilinear Square Operator and Commutator with Generalized Kernel

作　　者：陈晓莉 陈冬香[1] 朱红燕 Chen Xiaoli;Chen Dongxiang;Zhu Hongyan(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022)

机构地区：[1]江西师范大学数学与统计学院,南昌330022

出　　处：《数学物理学报（A辑）》2021年第4期954-967,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971209,11961032);江西省自然科学基金(20192BAB201003)。

摘　　要：该文研究了一类具有广义积分核的多线性平方算子,证明了该多线性平方算子T是(L^(p_1)(ω_1)×…×L^(p_m)(ω_m))到L^p(ν_w)上有界,其中1/p_1+…+1/p_m=1/p,Vw=i=1Лmw_(i)^(p/pi).同时该文还证明了多线性平方算子T和BMO函数生成的交换子T_(Σb)也是(L^(p_1)(ω_1)×…×L^(p_m)(ω_m))到L^p(ν_ω)上有界算子.最后证明了多线性平方算子T是L^∞×…×L^∞到BMO上的有界算子,推广了一些已知的结果.In this paper,the authors investigate some multilinear square operator with generalized kernel.They prove that the multilinear square operator T is bounded from(Lp1(ω1)×…×Lpm(ωm))into Lp(νω),where 1/p1+…+1/pm=1/p,Vw=i=1Лmw_(i)^(p/pi)the authors proved the commutator TΣb,generalized by multilinear square operator T and BMO function,is also bounded from(Lp1(ω1)×…×Lpm(ωm))into Lp(νω)上.Finally,the authors also prove the multilinear square operator T is bounded from L∞×…×L∞into BMO.Some known results are improved.

关 键 词：广义积分核 多线性平方算子 Sharp极大函数 交换子 权 

分 类 号：O174.2[理学—数学]