The domination principle for the sum of squares of vector fields (Q1109176)

Let G denote the Green function on a domain \(\Omega\) which belongs to a subelliptic operator of the form \[ L=\sum^{n}_{j=1}X^ 2_ j+\sum^{n}_{i,j=1}f_{ij}[X_ i,X_ j]+\sum^{n}_{j=1}f_ jX_ j+f_ 0, \] where the coefficients satisfy similar assumptions as in a paper of \textit{A. Sánchez-Calle} [Invent. Math. 78, 143-160 (1984; Zbl 0582.58004)]. Let \(\mu\), \(\nu\) Radon measures on \(\Omega\) such that the potential \(G\mu\) of \(\mu\) is finite and such that \(G\nu\geq G\mu\) holds on the support of \(\mu\). It is shown that this implies \(G\nu\geq G\mu\).