带粗糙核的多重Marcinkiewicz积分算子的Lp有界性

数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 914-927.

带粗糙核的多重Marcinkiewicz积分算子的L^p有界性

谢显华|肖新元|许绍元|马丽

1.赣南师范学院数学与计算机科学学院江西赣州 341000; 2.赣州三中江西赣州 341000

收稿日期:2011-04-28 修回日期:2012-08-06 出版日期:2012-10-25 发布日期:2012-10-25
基金资助:
国家自然科学基金(10961007)资助

L^p Boundedness of Multiple Marcinkiewicz Integral Operators with Rough Kernels

XIE Xian-Hua, XIAO Xin-Yuan, XU Shao-Yuan, MA Li

1.School of Mathematical Sciences, Gannan Normal University, Jiangxi Ganzhou 341000|2.The Third Middle School of Ganzhou, Jiangxi Ganzhou 341000

Received:2011-04-28 Revised:2012-08-06 Online:2012-10-25 Published:2012-10-25
Supported by:
国家自然科学基金(10961007)资助

摘要/Abstract

摘要：

主要利用Littlewood-Paley理论和Fourier变换估计研究在一些相当弱的尺寸条件下, 建立多重Marcinkiewicz积分算子的L^p有界性, 从而改进和推广前人的结论.

关键词: Marcinkiewicz积分, 粗糙核, Littlewood-Paley理论, Fourier变换估计

Abstract:

In this article, certain multiple Marcinkiewicz integral operators were studied. The L^p boundedness for these operators are established for some fixed p under some rather weak size by using Littlewood-Paley theory and Fourier transforms. the main results essentially improve and extend some known results.

Key words: Marcinkiewicz integral, Rough kernel, Littlewood-paley theory, Fourier transform estimate

中图分类号:

42B20

谢显华, 肖新元, 许绍元, 马丽. 带粗糙核的多重Marcinkiewicz积分算子的L^p有界性[J]. 数学物理学报, 2012, 32(5): 914-927.

XIE Xian-Hua, XIAO Xin-Yuan, XU Shao-Yuan, MA Li. L^p Boundedness of Multiple Marcinkiewicz Integral Operators with Rough Kernels[J]. Acta mathematica scientia,Series A, 2012, 32(5): 914-927.

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