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

Haïm Brezis, Jean Van Schaftingen, Po-Lam Yung

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 stron…