A new proof of the geometric Sobolev embedding for generalised Kolmogorov operators

Abstract

In this note we revisit a result in [9], where we established nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of Hörmander operators of Kolmogorov-type. We provide here a new proof which exploits a weak-type Sobolev embedding established in [11].