MMN-458
Global Hölder estimates for hypoelliptic operators with drift on homogeneous groups
Abstract
Let X0,X1, ...,Xq be left invariant real vector fields on the
homogeneous group G, satisfying H¨ormander’s condition on RN. Assume
that X1, ...,Xq be homogeneous of degree one and X0 be homogeneous of
degree two. In this paper we consider the following hypoelliptic operator
with drift
L =
Xq
i,j=1
aijXiXj + a0X0,
where (aij) is a constant matrix satisfying the elliptic condition in RN and
a0 2 R, and obtain Global H¨older estimates for L on G by establishing
several estimates of singular integrals.
Vol. 13 (2012), No. 2, pp. 337-347