Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfaces

Abstract

In this note, our aim is to show that families of smooth hypersurfaces of which are all "-close" enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical analysis, like Sobolev, Gagliardo-Nirenberg and "geometric" Calderón-Zygmund inequalities.