A Sobolev non embedding

Abstract

If $\Omega$ is a bounded domain in ${\mathbb{R}}^n$, $1\le q<p\le \infty$ and $s=0,1,2,\dots$, then we clearly have $W^{s,p}(\Omega )\subset W^{s,q}(\Omega )$. We prove that this property does not hold when $s$ in not an integer.