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arXiv · 2104.09867

Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail

Haïm Brezis·Jean Van Schaftingen·Po-Lam Yung
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Abstract

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

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Haïm Brezis, Jean Van Schaftingen, Po-Lam Yung. 2021-04-20. Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail. https://doi.org/10.1007/s00526-021-02001-w

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