Note on semigroups generated by positive Rockland operators on graded homogeneous groups
Tom 110 / 1994
Studia Mathematica 110 (1994), 115-126
DOI: 10.4064/sm-110-2-115-126
Streszczenie
Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let $p_t$ be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that $|p_1(x)| ≤ Cexp(-cτ(x)^{d/(d-1)})$. Moreover, if G is not stratified, more precise estimates of $p_1$ at infinity are given.
