A New Proof of the Geometric Sobolev Embedding for Generalised Kolmogorov Operators
摘要
In this note we revisit nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of Hörmander operators of Kolmogorov-type (Garofalo and Tralli, J Funct Anal 279:108591, 2020). We provide here a new proof which exploits a weak-type Sobolev embedding (Garofalo and Tralli, Math Ann 383: 1–38, 2022).