对任意给定的正整数m,Z+×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S(f)(x)=integral from n=(Rn)m to ∞[∏(i,j)∈S(bi(x)-bi(yj)(|x-y1|+···+|x-ym|)mn-α]multiply from...对任意给定的正整数m,Z+×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S(f)(x)=integral from n=(Rn)m to ∞[∏(i,j)∈S(bi(x)-bi(yj)(|x-y1|+···+|x-ym|)mn-α]multiply from j=1 to m[fj(yj)d→y ],其中d→y=dy1···dym.此框架下的交换子包含了以往研究的各类分数次积分算子的交换子,并蕴含了多线性背景下新的交换子形式.在上述非常一般框架下,本文给出带多重A→p,q权的多线性分数次积分算子的交换子Iα,→b,S(→f)的加权强型(Lp1(ω1)×···×Lpm(ωm),Lq(ν→ωq))估计和加权弱型端点估计.本文还得到更一般核条件下的上述结果.展开更多
In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
文摘对任意给定的正整数m,Z+×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S(f)(x)=integral from n=(Rn)m to ∞[∏(i,j)∈S(bi(x)-bi(yj)(|x-y1|+···+|x-ym|)mn-α]multiply from j=1 to m[fj(yj)d→y ],其中d→y=dy1···dym.此框架下的交换子包含了以往研究的各类分数次积分算子的交换子,并蕴含了多线性背景下新的交换子形式.在上述非常一般框架下,本文给出带多重A→p,q权的多线性分数次积分算子的交换子Iα,→b,S(→f)的加权强型(Lp1(ω1)×···×Lpm(ωm),Lq(ν→ωq))估计和加权弱型端点估计.本文还得到更一般核条件下的上述结果.
基金supported by National Natural Science Foundation of China (Grant No.10701010) the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金supported by National Natural Science Foundation of China (Grant No.10571015) Research Fund for the Doctoral Program of Higher Education of China (Grant No.20050027025)
文摘In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
