A note on the maximal operator on Banach function spaces

2024/04/24 by Andrei K. Lerner, Lerner, Andrei K.
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2404.15671

openalex publication_date 2024/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we answer positively to two conjectures proposed by Nieraeth (2023) about the maximal operator on rescaled Banach function spaces. We also obtain a new criterion saying when the maximal operator bounded on a Banach function space X is also bounded on the associate space X'.

Related

• Hardy-Littlewood maximal operator on the associate space of a Banach function space
• Recent progress on Monotone Operator Theory
• Lectures on maximal monotone operators
• On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive Banach spaces
• Sum of two maximal monotone operators in a general Banach space is maximal