双线性Fourier乘子交换子的有界性与紧性
Boundedness and Compactness for Commutators of Bilinear Fourier Multipliers
假定Tσ是关于乘子σ的双线性Fourier乘子算子,其中σ满足如下Sobolev正则条件:对某个s∈(n,2n],有supk∈Z||σk||Ws (R2n).对于p1,p2,p∈(1,∞)且满足1/p=1/p1+1/p2和ω=(ω1,ω2)∈Ap/t(R2n),建立了Tσ及其与函数b=(b1,b2)∈(BMO (Rn))2生成的交换子Tσ,b由Lp1,λ (ω1)×Lp2,λ(ω2)到Lp,λ(νw)的有界性;同时,在b1,b2∈CMO (Rn)(Cc∞(Rn)在BMO拓扑下的闭包)的条件下,证明交换子Tσ,b是Lp1,λ(ω1)×Lp2,λ(ω2)到Lp,λ(νw)的紧算子.为了得到主要结果,我们先后建立了几个双(次)线性极大函数在加多权Morrey空间上的有界性以及该空间中准紧集的判定.
Let Tσ be the bilinear Fourier multiplier operator associated with multiplier σ satisfying the Sobolev regularity that supk∈Z ||σk||Ws (R2n)<∞ for some s∈(n,2n].We give the boundedness of Tσ and the commutators Tσ,b generated by Tσ and b=(b1,b2)∈(BMO (Rn))2,as well as the compactness of Tσ,b (if b1,b2∈CMO (Rn),the BMO-closure of Cc∞ (Rn)) from Lp1,λ(ω1)×Lp2,λ(ω2) to Lp,λ(νw) for appropriate indices p1,p2,p∈(1,∞)(1/p=1/p1+1/p2) and multiple weights ω=(ω1,ω2)∈Ap/t (R2n).The main ingredient is to establish the multiple weighted estimates for the variants of certain multi (sub) linear maximal operators on the weighted Morrey spaces,and a sufficient condition for a subset in the weighted Morrey spaces to be a strongly precompact set,which are in themselves interesting.
双线性Fourier乘子 / 交换子 / 双(次)线性极大算子 / 紧性 / 加权Morrey空间 {{custom_keyword}} /
bilinear Fourier multipliers / commutators / bi (sub) linear maximal operators / compactness / weighted Morrey spaces {{custom_keyword}} /
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国家自然科学基金资助项目(11371295, 11471041);福建省自然科学基金项目(2015J01025)
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