Abstract
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.
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Acknowledgements
This work was carried out during two visits of J. Van Schaftingen to Rutgers University. He thanks H. Brezis for the invitation and the Department of Mathematics for its hospitality. P-L. Yung was partially supported by a Future Fellowship FT200100399 from the Australian Research Council. H. Brezis is grateful to C. Sbordone who communicated to him the interesting paper [16] by Greco and Schiattarella which triggered our work.
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Brezis, H., Van Schaftingen, J. & Yung, PL. Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail. Calc. Var. 60, 129 (2021). https://doi.org/10.1007/s00526-021-02001-w
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DOI: https://doi.org/10.1007/s00526-021-02001-w