1. On Wolff's L 5/2-Kakeya maximal inequality in ℝ3
- Author
-
Jiqiang Zheng, Changxing Miao, and Jianwei Yang
- Subjects
Combinatorics ,Inequality ,Applied Mathematics ,General Mathematics ,media_common.quotation_subject ,Geometric combinatorics ,Mathematics ,media_common - Abstract
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.
- Published
- 2014