High order regularity for subelliptic operators on Lie groups of polynomial growth

Dungey, Nick

Rev. Mat. Iberoamericana, Tome 21 (2005) no. 2, p. 929-996 / Harvested from Project Euclid

Résumé

Let $G$ be a Lie group of polynomial volume growth, with Lie algebra $\mbox{\gothic g}$. Consider a second-order, right-invariant, subelliptic differential operator $H$ on $G$, and the associated semigroup $S_t = e^{-tH}$. We identify an ideal $\mbox{\gothic n}'$ of $\mbox{\gothic g}$ such that $H$ satisfies global regularity estimates for spatial derivatives of all orders, when the derivatives are taken in the direction of $\mbox{\gothic n}'$. The regularity is expressed as $L_2$ estimates for derivatives of the semigroup, and as Gaussian bounds for derivatives of the heat kernel. We obtain the boundedness in $L_p$, $1

Détail

Publié le : 2005-03-14
Classification:  Lie group,  subelliptic operator,  heat kernel,  Riesz transform,  regularity estimates,  22E30,  35B65,  58J35