具有齐性核Marcinkiewicz积分交换子的Lipschitz估计  

LIPSCHITZ ESTIMATES FOR COMMUTATORS OF MARCINKIEWICZ INTEGRAL WITH HOMOGENEOUS KERNEL

作　　者：陈冬香[1] 陈杰诚[2] 

机构地区：[1]杭州师范学院数学系,杭州310012 [2]浙江大学数学系,杭州310028

出　　处：《数学年刊（A辑）》2005年第3期325-332,共8页Chinese Annals of Mathematics

基　　金：教育部博士点基金(No.20030335019);国家科委973(No.RC971077;No.1999075105);杭州师范学院博 士启动基金资助的项目.

摘　　要：本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)上的有界算子并且也是Lp(Rn)到Lq(Rn)上的有界算子.In this paper, the authors consider the commutator of Marcinkiewicz integral defined by μΩb(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2dt/t31/2,where Fb,t(f)(x)=integral from n=|x-y|≤ t to (Ω(x-y)/|x-y|n-1[b(x)- b(y)] f(y)dy and b ∈ Aβ, and show that the operator μΩ,b is bounded from Lp(Rn) into Fβ,∞ p(Rn), and is also from Lp(Rn into Lq(Rn).

关 键 词：MARCINKIEWICZ积分 L^s-Dini条件 交换子 Triebel—Lizorkin空间 

分 类 号：O177.6[理学—数学]