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<p>In this note we answer positively to two conjectures proposed by Nieraeth (J Funct Anal 285:109, 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 <i>X</i> is also bounded on the associate space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2015_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(X'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>X</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>.</p>

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A Note on the Maximal Operator on Banach Function Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月22日

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  • Andrei K. Lerner

摘要

In this note we answer positively to two conjectures proposed by Nieraeth (J Funct Anal 285:109, 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 \(X'\) X ′ .