带参数的抛物型Marcinkiewicz积分的L^2(R^n)有界性  

L^2(R^n) Boundedness of Parametric Parabolic Marcinkiewicz Integral

作　　者：赵志云[1] 牛耀明[1] 

机构地区：[1]包头师范学院数学科学学院,内蒙古包头014030

出　　处：《内蒙古大学学报（自然科学版）》2012年第2期113-117,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11161042;11071250)

摘　　要：利用核的分解技术和Fourier变换估计,得到了粗糙核带参数的抛物型Marcinkiewicz积分μσΩ(f)的L2(Rn)有界性.作为应用得到了分别与Littlewood-Paley gλ*函数和Lusin面积函数相应的参数型Marcinkiewicz函数μΩ*,λ,σ和μσΩ,S的L2(Rn)有界性.Using kernel decomposition technique and Fourier transform estimate,the L2(Rn) boundedness is obtained for a class of parametric parabolic Marcinkiewicz Integral μσΩ(f) with a rough kernel.As an application,the L2(Rn) boundedness of μ*,σΩ,λ and μσΩ,S are also obtained.Here μ*,σΩ,λ and μσΩ,S are parametric Marcinkiewicz integrals correspending to the Littlewood-Paley g*λ-function and the Lusin area function,respectively.

关 键 词：MARCINKIEWICZ积分 抛物型Marcinkiewicz积分 粗糙核 

分 类 号：O174.2[理学—数学]