Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on we prove that it is closed on each of the -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the -spaces, p ∈ [1,∞]. Further extensions of these results to nonhomogeneous operators and general representations are also given.
@article{bwmeta1.element.bwnjournal-article-cmv67i2p197bwm,
author = {Pascal Auscher and A. ter Elst and Derek Robinson},
title = {On positive Rockland operators},
journal = {Colloquium Mathematicae},
volume = {67},
year = {1994},
pages = {197-216},
zbl = {0856.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv67i2p197bwm}
}
Auscher, Pascal; ter Elst, A.; Robinson, Derek. On positive Rockland operators. Colloquium Mathematicae, Tome 67 (1994) pp. 197-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv67i2p197bwm/
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