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<p>We characterize some weighted one-dimensional Poincaré inequalities on Banach function spaces, generalizing in this way Chua and Wheeden’s theorem in the case <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_939_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\le q\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≤</mo> <mi>q</mi> </mrow> </math></EquationSource> </InlineEquation>. As particular cases, we get the characterizations of some weighted Orlicz-Poincaré inequalities and Poincaré inequalities in variable Lebesgue spaces. We also get a new result on weighted weak-type inequalities of this kind.</p>

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Weighted one-dimensional Poincaré inequalities in Banach function spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月22日

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  • P. Ortega Salvador,
  • C. Ramírez Torreblanca

摘要

We characterize some weighted one-dimensional Poincaré inequalities on Banach function spaces, generalizing in this way Chua and Wheeden’s theorem in the case \(p\le q\) p ≤ q . As particular cases, we get the characterizations of some weighted Orlicz-Poincaré inequalities and Poincaré inequalities in variable Lebesgue spaces. We also get a new result on weighted weak-type inequalities of this kind.