A recursive bound for a Kakeya-type maximal operator

2005/11/26 by Richard Oberlin, Oberlin, Richard · 2 citations
Mathematics · #42B25 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #math.CA #msc:42B25

paper · pdf · doi:10.48550/arxiv.math/0511646

15 pages, no figures

arxiv created 2005/11/26 · openalex publication_date 2005/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A (d,k) set is a subset of R^d containing a translate of every k-dimensional plane. Bourgain showed that for 2^k-1+k ≥ d, every (d,k) set has positive Lebesgue measure. We give an L^p bound for the corresponding maximal operator.

Cited by

• Bounds for Kakeya-type maximal operators associated with k-planes
• An incidence bound for k-planes in Fⁿ and a planar variant of the Kakeya maximal function

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