PROBABILISTIC CONSTRUCTION OFKAKEYA-TYPE SETS IN ℝ2 ASSOCIATED TO SEPARATED SETS OF DIRECTIONS

Paul Hagelstein; Blanca Radillo-Murguia; Alexander Stokolos

doi:10.1215/00127094-2025-0025

PROBABILISTIC CONSTRUCTION OFKAKEYA-TYPE SETS IN ℝ² ASSOCIATED TO SEPARATED SETS OF DIRECTIONS

Paul Hagelstein
, Blanca Radillo-Murguia
, Alexander Stokolos

Mathematical Sciences

Baylor University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We provide a condition on a set of directions ensuring Ω ⊂ S¹ ensuring that the associated directional maximal operator M_Ω is unbounded on L^p(R²) for every 1 ≤ p < The techniques of proof extend ideas of Bateman and Katz involving probabilistic construction of Kakeya-type sets using sticky maps and Bernoulli percolation.

Original language	English
Pages (from-to)	185-198
Number of pages	14
Journal	Duke Mathematical Journal
Volume	175
Issue number	2
DOIs	https://doi.org/10.1215/00127094-2025-0025
State	Published - Feb 2026

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General Mathematics

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10.1215/00127094-2025-0025

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abstract = "We provide a condition on a set of directions ensuring Ω ⊂ S1 ensuring that the associated directional maximal operator MΩ is unbounded on Lp(R2) for every 1 ≤ p < The techniques of proof extend ideas of Bateman and Katz involving probabilistic construction of Kakeya-type sets using sticky maps and Bernoulli percolation.",

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AB - We provide a condition on a set of directions ensuring Ω ⊂ S1 ensuring that the associated directional maximal operator MΩ is unbounded on Lp(R2) for every 1 ≤ p < The techniques of proof extend ideas of Bateman and Katz involving probabilistic construction of Kakeya-type sets using sticky maps and Bernoulli percolation.

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PROBABILISTIC CONSTRUCTION OFKAKEYA-TYPE SETS IN ℝ² ASSOCIATED TO SEPARATED SETS OF DIRECTIONS

Abstract

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