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<p>This paper is interested in stability estimates for a class of one-dimensional Gagliardo–Nirenberg–Sobolev inequalities obtained by Nagy (Acta Univ Szeged Sect Sci Math 10:64–74, 1941) with the aid of the weighted Sobolev inequality on half-spaces demonstrated by Bakry et al. (Analysis and geometry of Markov diffusion operators, Springer, Cham, 2014). Our results fill the gap of Nguyen (J Funct Anal 277:2179–2208, 2019) in which the author established some quantitative estimates for a class of Gagliardo–Nirenberg–Sobolev inequalities when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_1970_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Stability Estimates for the Sharp One-Dimensional Gagliardo–Nirenberg–Sobolev Inequalities

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Xiao-Ping Chen,
  • Chun-Lei Tang

摘要

This paper is interested in stability estimates for a class of one-dimensional Gagliardo–Nirenberg–Sobolev inequalities obtained by Nagy (Acta Univ Szeged Sect Sci Math 10:64–74, 1941) with the aid of the weighted Sobolev inequality on half-spaces demonstrated by Bakry et al. (Analysis and geometry of Markov diffusion operators, Springer, Cham, 2014). Our results fill the gap of Nguyen (J Funct Anal 277:2179–2208, 2019) in which the author established some quantitative estimates for a class of Gagliardo–Nirenberg–Sobolev inequalities when \(n\ge 2\) n ≥ 2 .