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5. 沿实解析子流形的粗糙核Marcinkiewicz积分

沿实解析子流形的粗糙核Marcinkiewicz积分

来源 :数学学报：中文版 | 被引量 : 0次 | 上传用户：qq2285387

【摘 要】

：

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.

【作 者】

：

刘荣辉 刘风 伍火熊 薛庆营 

【机 构】

：

厦门大学数学科学学院,山东科技大学数学与系统科学学院,北京师范大学数学科学学院

【出 处】

：

数学学报：中文版

【发表日期】

：

2021年4期

【关键词】

：

MARCINKIEWICZ积分 极大算子 粗糙核 实解析子流形 

【基金项目】

：

国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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论文部分内容阅读

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.

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