On Wolff's L5/2-Kakeya maximal inequality in ℝ3

Changxing Miao; Jianwei Yang; Jiqiang Zheng

doi:10.1515/forum-2013-0160

On Wolff's L^5/2-Kakeya maximal inequality in ℝ³

Changxing Miao
, Jianwei Yang
, Jiqiang Zheng

IAPCM
China Academy of Engineering Physics

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

We reprove Wolff's L^5/2-bound for the ℝ³-Kakeya maximal function without appealing to the argument of induction on scales. The main ingredient in our proof is an adaptation of Sogge's strategy used in the work on Nikodym-type sets in curved spaces. Although the equivalence between these two type maximal functions is well known, our proof may shed light on some new geometric observations which is interesting in its own right.

源语言	英语
页（从-至）	3053-3077
页数	25
期刊	Forum Mathematicum
卷	27
期	5
DOI	https://doi.org/10.1515/forum-2013-0160
出版状态	已出版 - 1 9月 2015
已对外发布	是

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N2 - We reprove Wolff's L5/2-bound for the ℝ3-Kakeya maximal function without appealing to the argument of induction on scales. The main ingredient in our proof is an adaptation of Sogge's strategy used in the work on Nikodym-type sets in curved spaces. Although the equivalence between these two type maximal functions is well known, our proof may shed light on some new geometric observations which is interesting in its own right.

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KW - geometric combinatorics

KW - multiplicity argument

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On Wolff's L5/2-Kakeya maximal inequality in ℝ3

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On Wolff's L^5/2-Kakeya maximal inequality in ℝ³