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<p>We establish the Gagliardo–Nirenberg–Sobolev inequalities in subhyperbolic domains and, conversely, under an additional weak slice condition, we demonstrate that a domain supporting such inequalities must be classified as a subhyperbolic domain. This extends the work of Gehring and Martio for the local Lipschitz extension/embedding and also Buckley, Koskela, and Stanoyevitch for the Sobolev embedding.</p>

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Characterizations of domains supporting Gagliardo–Nirenberg–Sobolev inequalities via subhyperbolicity

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • Zeming Wang,
  • Dachun Yang,
  • Yuan Zhou

摘要

We establish the Gagliardo–Nirenberg–Sobolev inequalities in subhyperbolic domains and, conversely, under an additional weak slice condition, we demonstrate that a domain supporting such inequalities must be classified as a subhyperbolic domain. This extends the work of Gehring and Martio for the local Lipschitz extension/embedding and also Buckley, Koskela, and Stanoyevitch for the Sobolev embedding.