一类平方函数的加幂权有界性

A class of square functions with power weights

本文讨论平方函数 gΨ(f )和幂权 Lp 有界性 ,其中Ψ (x) =Ω (x′) g(|x|) ,Ω∈ H1(Sn-1) ,且g(|x|)满足一定的条件 .作为推论 ,本文得到了 Marcinkiewicz积分μΩ(f )加幂权的 Lp

For \$Ω∈H\+1(S\+\{n-1\}) \%and suitable\% g∈L\+1(R\+1\-+,r\+\{n-1\} \%d\%r),\%the\% L\+p(|x|\+α\%d\%x) \%boundedness of\% g\-Ψ\% was obtained,where\% Ψ(x)=Ω(x′)g(|x|).\%As a corollary,the\% L\+p(|x|\+α\%d\%x) \%boundedness of the Marcinkiewicz integral operator\% μ\-Ω(f)\% was obtained.The\% L\+2(|x|\+α\%d\%x) \%boundedness of\% μ\-Ω(f)\% for\% Ω\$ being introduced in the paper\ was also given.