Abstract

We prove that the best constant in the Folland–Stein embedding theorem on Carnot groups is achieved. This implies the existence of a positive solution of the Yamabe-type equation on Carnot groups. The second goal of the paper is to show a certain regularity of the Green’s function and solutions of the Yamabe equation involving the sub-Laplacian near the characteristic boundary of a domain in the considered groups.

Keywords

subelliptic regularity, Sobolev embedding, Carnot groups

Mathematical Subject Classification

Primary: 35J70

Authors