- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:44
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
21
2005
3
High order regularity for subelliptic operators on Lie groups of polynomial growth
Nick
Dungey
Macquarie University, SYDNEY, NSW, AUSTRALIA
Lie group, subelliptic operator, heat kernel, Riesz transform, regularity estimates
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
Topological groups, Lie groups
Partial differential equations
Global analysis, analysis on manifolds
General
929
996
10.4171/RMI/441
http://www.ems-ph.org/doi/10.4171/RMI/441