Geodesic
On positive Rockland operators
Colloquium Mathematicum, Tome 67 (1994) no. 2, pp. 197-216.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on $L_p(G;dg)$. Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on $L_2$ we prove that it is closed on each of the $L_p$-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 $L_p$-spaces, p ∈ [1,∞]. Further extensions of these results to nonhomogeneous operators and general representations are also given.
DOI : 10.4064/cm-67-2-197-216

Pascal Auscher 1 ; A. ter Elst 1 ; Derek Robinson 1

1 
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Pascal Auscher; A. ter Elst; Derek Robinson. On positive Rockland operators. Colloquium Mathematicum, Tome 67 (1994) no. 2, pp. 197-216. doi : 10.4064/cm-67-2-197-216. http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-197-216/

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