Weighted Estimates For Littlewood-Paley Operators With Rough Kernels

In this dissertation, we shall deal with the weighted estimates of the Littlewood-Paley operators with rough kernels on some function spaces. The main results are as follows:In the chapter1, we obtain that the parametrized area integral μΩ,Sρ and gλ*function μλ*,ρ are bounded from the weighted weak Hardy space WωΓ(Rn) to the weighted weak Lebesgue space WLωΓ(Rn) as Ω satisfies a class of the integral Dini condition, respectively.In the chapter2, as the kernel Ω∈Lq(Sn-1)(1<q≤oo) is homogeneous of degree zero and has mean value zero on Sn-1, the boundedness of two classes of the Littlewood-Paley operators with rough kernel is obtained on the weighted Morrey spaces Lp,k(ω).In the chapter3, we prove the boundedness of the Lusin-area integral μΩ,S and Littlewood-Paley functions μΩ and Ωλ*on the weighted Amalgam spaces(Lωq,Lp)α(Rn) as1<q≤α<P≤∞.