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<p>The sharp convex Lorentz–Sobolev inequality is due to Ludwig et al. (Math Ann 350:169–197, 2011) by using the notion of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1774_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> convexification of level sets. In this paper, the anisotropic version and the Grassmannian form of this inequality are obtained.</p>

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Strengthened forms of the convex Lorentz–Sobolev inequality

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Haiwei Ye,
  • Yangyi Lu,
  • Qingzhong Huang

摘要

The sharp convex Lorentz–Sobolev inequality is due to Ludwig et al. (Math Ann 350:169–197, 2011) by using the notion of the \(L_p\) L p convexification of level sets. In this paper, the anisotropic version and the Grassmannian form of this inequality are obtained.