Reverse superposition estimates in Sobolev spaces

Abstract

We study when and how the norm of a function $u$ in the homogeneous Sobolev spaces ${\dot{W}}^{s,p}({\mathbb{R}}^n,{\mathbb{R}}^m)$, with $p\ge 1$ and either $s=1$ or $s>1/p$, is controlled by the norm of composite function $f\circ u$ in the same space.

arXiv comment7 pages, minor corrections