非齐次粗糙核参数型Marcinkiewicz算子的H~p有界性

设Ω是球面上函数,b是径向函数,ρ是实部正的复数;设Ψ为C~2(0,∞))的递增凸函数,Ψ(0)=0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,b)~ρ,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,Ψ,b)~ρ,给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μ_(Ω,b)~ρ和μ_(Ω,Ψ,b)~ρ在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作.

Hp Bounds for Parametric Marcinkiewicz Operators with Nonhomogenous Rough Kernels

Let Ω be a function on the unit sphere and b a radial function, and ρ be a complex parameter with Re (ρ)>0. Let Ψ be in C²(0,∞)), convex, and increasing function with Ψ(0) = 0. The parametric Marcinkiewicz operator μ^ρ_{Ω, b} with nonhomogenous rough kernel and the rough Marcinkiewicz operator μ^ρ_{Ω, Ψ, b} related to a surface of revolutions are considered in this paper, we prove the boundedness of these Marcinkiewicz operators on Hardy spaces and weak Hardy spaces under the minimum smooth conditions for the rough kernels Ω and b. The results in this paper extend as well as improve previously known results.