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

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.

Fixed up some typos. arXiv admin note: text overlap with arXiv:2003.05216

References in corpus (1)

• A surprising formula for Sobolev norms

Cited by in corpus (1)

• New estimates for a class of non-local approximations of the total variation