Endpoint multiplier theorems of Marcinkiewicz type

2000/01/09 by Terence Tao, Tao, Terence, Jim Wright +2
Mathematics · #42B15 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #math.CA #msc:42B15

paper · pdf · doi:10.48550/arxiv.math/0001050

28 pages, no figures, submitted to Revista Mat. Iber

arxiv created 2000/01/09 · openalex publication_date 2000/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish sharp (H¹, L^1,q) and local (L log^r L, L^1,q) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H¹ to L^1,∞ and L log^1/2 L to L^1,∞, and that these estimates are sharp.

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