The Kakeya maximal operator on the variable Lebesgue spaces

2014/04/10 by Hiroki Saito, Hitoshi Tanaka, Saito, Hiroki +1
Mathematics · #42B25 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42B25 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1404.2690

arxiv created 2014/04/10 · openalex publication_date 2014/04/10 · arxiv updated 2014/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We shall verify the Kakeya (Nikodym) maximal operator K_N, N≫ 1, is bounded on the variable Lebesgue space L^p(⋅)(ℝ²) when the exponent function p(⋅) is N-modified locally log-Hölder continuous and log-Hölder continuous at infinity.

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