On a non-standard characterization of the A_p condition

2024/09/12 by Andrei K. Lerner, Lerner, Andrei K.
Mathematics · #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2409.07781

openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical Muckenhoupt's A_p condition is necessary and sufficient for the boundedness of the maximal operator M on L^p(w) spaces. In this paper we obtain another characterization of the A_p condition. As a result, we show that some strong versions of the weighted L^p(w) Coifman--Fefferman and Fefferman--Stein inequalities hold if and only if w∈ A_p. We also give new examples of Banach function spaces X such that M is bounded on X but not bounded on the associate space X'.

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