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中国科学院大学学报 ›› 2018, Vol. 35 ›› Issue (4): 433-437.DOI: 10.7523/j.issn.2095-6134.2018.04.001

• 数学与物理学 •    下一篇

迭代的哈代-李特伍德极大函数

王泽群, 燕敦验   

  1. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2017-03-28 修回日期:2017-04-26 发布日期:2018-07-15
  • 通讯作者: 燕敦验
  • 基金资助:
    Supported by National Natural Science Foundation of China(11471039, 11271162)

Iterated Hardy-Littlewood maximal function

WANG Zequn, YAN Dunyan   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2017-03-28 Revised:2017-04-26 Published:2018-07-15
  • Supported by:
    Supported by National Natural Science Foundation of China(11471039, 11271162)

摘要: 研究迭代的非中心型哈代-李特伍德极大函数和迭代的中心型哈代-李特伍德极大函数。证明迭代极大函数的极限是极大算子的一个不动点。作为不动点理论的一个应用,最终得到,对于非中心型哈代-李特伍德极大算子,这个不动点处处为||f||。对于中心型哈代-李特伍德极大算子,仅在n=1,2时有相同的结果。

关键词: 哈代-李特伍德极大函数, 不动点, 迭代的哈代-李特伍德极大函数

Abstract: In the paper, we investigate the iterated non-centered Hardy-Littlewood maximal function and the iterated centered Hardy-Littlewood maximal function. We prove that the limit of the iterated maximal function is just a fixed point of maximal operator. As an application of the fixed point theory, we finally obtain that the fixed point is||f|| for non-centered Hardy-Littlewood maximal operator. The same is true for the centered Hardy-Littlewood maximal operator only for n=1,2.

Key words: Hardy-Littlewood maximal function, fixed point, iterated Hardy-Littlewood maximal function

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