Harnack Inequality on Homogeneous Spaces
Abstract
Description
We consider a homogeneous space $X=(X,d,m) $ of dimension $ν\geq1$ and a local regular Dirichlet form in $L^{2}(X,m) .$ We prove that if a Poincaré inequality holds on every pseudo-ball $B(x,R) $ of $X$, then an Harnack's inequality can be proved on the same ball with local characteristic constant $c_{0}$ and $c_{1}$
To appear in Annali di Matematica Pura e Applicata
To appear in Annali di Matematica Pura e Applicata