Harnack Inequality on Homogeneous Spaces

Details Harnack Inequality on Homogeneous Spaces Harnack Inequality on Homogeneous Spaces

1996-04-03

arxiv.org/abs/funct-an/9604003v3

Mathematics

Functional Analysis

To appear in Annali di Matematica Pura e Applicata

Scientific paper

We consider a homogeneous space $X=(X,d,m) $ of dimension $\nu\geq1$ and a
local regular Dirichlet form in $L^{2}(X,m) .$ We prove that if a Poincar\'{e}
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 $c_{1}$

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