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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（log L）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 some γ ∈ (1, ∞] and the sphere kernel Ω ∈ 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 Ω ∈ L(log L) 1/2 (Sn-1) or Ω ∈ Bq(0,-1/2)(Sn-1) for some q > 1. Meanwhile, the Lp estimates for the related maximal rough Marcinkiewicz integrals are also considered.
Marcinkiewicz积分 / 极大算子 / 粗糙核 / 实解析子流形 {{custom_keyword}} /
Marcinkiewicz integrals / maximal operators / rough kernels / real-analytic submanifolds {{custom_keyword}} /
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家自然科学基金资助项目（11701333，11771358，11871101，11671039，11871101）；中德合作研究项目（11761131002）
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