Brezis, HaimVan Schaftingen, JeanYung, Po-Lam2023-05-22Brezis, 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-w0944-2669http://hdl.handle.net/1885/292095In the cases where there is no Sobolev-type or Gagliardo–Nirenberg-type fractional estimate involving |u|Wsp, we establish alternative estimates where the strong Lp norms are replaced by Lorentz norms.P-L. Yung was partially supported by a Future Fellowship FT200100399 from the Australian Research Council.application/pdfen-AU© 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature2021-06-2910.1007/s00526-021-02001-w2022-03-20