Herz空间上Littlewood-Paley g函数的加权弱有界性  

Weak Boundedness for Littlewood-Paley g Functions on Weighted Herz Spaces

作　　者：孙晓华[1] 赵凯[1] 李加锋[1] 郝春燕[1] 李兰兰[1] 

机构地区：[1]青岛大学数学科学学院,山东青岛266071

出　　处：《青岛大学学报（自然科学版）》2009年第4期21-24,共4页Journal of Qingdao University(Natural Science Edition)

摘　　要：研究了Littlewood-Paley g函数在加权Herz空间上的弱有界性。利用加权Herz空间的分解理论及几个不等式,证明了若ω1,2ω∈A1,当0<α≤n(1-1/q)时,gψ是.Kq,αp(1ω,ω2)到W.Kqα,p(ω1,2ω)上的有界算子,并且当0<α<n(1-1/q)时,gψ在加权Herz空间上具有强有界性。此结果丰富了Littlewood-Paleyg函数的有界性理论。The weak boundedness on weighted Herz spaces is considered for Littlewood-Paley g functions. By the decomposition of weighted Herz space and several inequalities, it is obtained that gφ is boundedness from Kq^α,p（ω1,ω2） to WKq^α,p（ω1,ω2）, then for ω1,ω2 ∈A1, when 0〈α≤n（1- 1/q）, and gφ is strong boundedness on weighted Herz spaces when 0〈α〈n（1-1/q）. The result enriches the boundedness theory of Littlewood-Paley g functions.

关 键 词：Littlewood—Paley G函数 加权HERZ空间 加权弱Herz空间 

分 类 号：O174.2[理学—数学]