A sharp subelliptic Sobolev embedding theorem with weights

TL;DR

This paper establishes sharp weighted subelliptic Sobolev inequalities, providing potential estimates that improve understanding of smoothing effects and behavior away from characteristic varieties.

Contribution

It introduces new potential estimates leading to optimal local subelliptic Sobolev inequalities and their quantitative improvements.

Findings

Proved a local subelliptic Sobolev inequality with optimal smoothing.

Derived a variant showing quantitative improvements away from characteristic varieties.

Established potential estimates relevant to subelliptic Sobolev inequalities.

Abstract

The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal amount of smoothing, as well as a variant of that which describes quantitatively an improvement of the inequality as one gets away from certain characteristic varieties.