Endpoint sparse bounds for Walsh-Fourier multipliers of Marcinkiewicz type

2018/05/15 by Chen, Wei, Amalia Culiuc, Francesco Di Plinio +6
Mathematics · #42B20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1805.06060

openalex publication_date 2018/05/15 · openalex created_date 2018/06/01 · openalex updated_date 2026/07/28

Abstract

We prove endpoint-type sparse bounds for Walsh-Fourier Marcinkiewicz multipliers and Littlewood-Paley square functions. These results are motivated by conjectures of Lerner in the Fourier setting. As a corollary, we obtain novel quantitative weighted norm inequalities for these operators. Among these, we establish the sharp growth rate of the L^p weighted operator norm in terms of the A_p characteristic in the full range 1

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