沿实解析子流形的粗糙核Marcinkiewicz积分

Marcinkiewicz Integrals with Rough Kernels Along Real-analytic Submanifolds

本文研究沿实解析子流形的粗糙核Marcinkiewicz积分的Lp映射性质,假设径向核h∈Δγ(R+)(γ∈(1,∞])与球面核Ω∈Lq(Sn-1)(q∈(1,2]),建立了这类算子的Lp有界性.而且,通过外插的方法,在一些最佳的球面尺寸条件Ω∈L(logL)1/2(Sn-1)或Ω∈Bq(0,-1/2)(Sn-1)(q>1)下,获得了相应的Lp界.与此同时,也考虑了相关极大粗糙核Marcinkiewicz积分的Lp估计.

This paper is devoted to studying the Lp-mapping properties of the rough Marcinkiewicz integrals with rough kernels along real-analytic submanifolds.Under assuming that the radial kernel h∈Δγ(R+)for someγ∈(1,∞]and the sphere kernelΩ∈Lq(Sn-1)for some q∈(1,2],the Lp-boundedness for such operators are established.Furthermore,by the extrapolation arguments,the corresponding Lp-bounds are obtained under some optimal size conditions on the unit sphere∈L(logL)1/2(Sn-1)orΩ∈Bq(0,-1/2)(Sn-1)for some q>1.Meanwhile,the Lp estimates for the related maximal rough Marcinkiewicz integrals are also considered.