On Sobolev and capacitary inequalities for contractive Besov spaces over \(d\)-sets
The authors derive Sobolev inequalities for Besov spaces from a metric property of the Bessel capacity on \(\mathbb{R}^n\). First, they extend Kaimanovitch's result on the equivalence of Sobolev and capacity inequalities for contractive \(p\)-norms in a general setting allowing unbounded Lévy kernels. Then they apply a simple part of the Jonsson-Wallin trace theorem to Besov spaces.
scientific article; zbMATH DE number 1901234