The sobolev embeddings are usually sharp

Abstract

Let $x_0\in {ℝ}^d$; we study the Hölder regularity at $x_0$ of a generic function of the Sobolev space $L^{p,s}\left({ℝ}^d\right)$ and of the Besov space $B_p^{s,q}\left({ℝ}^d\right)$ for $s-d/p>0$. The setting for genericity is supplied here by HP-residual sets.