In the cases where there is no Sobolev-type or Gagliardo–Nirenberg-type fractional estimate involving \({|u |}_{W^{s,p}}\), we establish alternative estimates where the strong \(L^p\) norms are replaced by Lorentz norms.

中文翻译：

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当分数 Sobolev、Gagliardo 和 Nirenberg 估计失败时去洛伦兹

在没有涉及\({|u |}_{W^{s,p}}\) 的Sobolev 型或 Gagliardo-Nirenberg 型分数估计的情况下，我们建立替代估计，其中强\(L^ p\)范数被洛伦兹范数取代。