A Bourgain-Brezis-Mironescu characterization of higher order Besov-Nikol'skii spaces

Abstract

We study a class of nonlocal functionals in the spirit of the recent characterization of the Sobolev spaces $W^{1,p}$ derived by Bourgain, Brezis and Mironescu. We show that it provides a common roof to the description of the $BV({\mathbb{R}}^N)$, $W^{1,p}({\mathbb{R}}^N)$, $B_{p,\infty }^s({\mathbb{R}}^N)$ and $C^{0,1}({\mathbb{R}}^N)$ scales and we obtain new equivalent characterizations for these spaces. We also establish a non-compactness result for sequences and new (non-)limiting embeddings between Lipschitz and Besov spaces which extend the previous known results.

Accepted for publication in "Annales de l'Institut Fourier"

Cited by in corpus (1)

• On restrictions of Besov functions