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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 5

Issues

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

Changxing Miao
  • Institute of Applied Physics and Computational Mathematics, Huayuan Road No. 6, Haidian District, P.O. Box 8009, Beijing 100088, P. R. China
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/ Jianwei Yang
  • The Graduate School of China Academy of Engineering Physics, Huayuan Road No. 6, Haidian District, P.O. Box 2101, Beijing 100088, P. R. China
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/ Jiqiang Zheng
  • The Graduate School of China Academy of Engineering Physics, Huayuan Road No. 6, Haidian District, P.O. Box 2101, Beijing 100088, P. R. China
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Published Online: 2014-01-21 | DOI: https://doi.org/10.1515/forum-2013-0160

Abstract

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.

Keywords: Kakeya maximal function; multiplicity argument; geometric combinatorics

MSC: 42B25

About the article

Received: 2013-10-01

Revised: 2013-12-23

Published Online: 2014-01-21

Published in Print: 2015-09-01


Funding Source: NSF of China

Award identifier / Grant number: 11171033

Funding Source: NSF of China

Award identifier / Grant number: 11231006

Funding Source: NSF of China

Award identifier / Grant number: 11371059

Funding Source: Beijing Center for Mathematics and Information Interdisciplinary Sciences


Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 3053–3077, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0160.

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