齐次群上带漂移项亚椭圆算子的整体Sobolev-Morrey估计

Global Sobolev-Morrey estimates for hypoelliptic operators with drift on homogeneous groups

设G是一个齐次群,X0,X1,X2,...,Xp0为G上满足Ho¨rmander秩条件的实左不变向量场且X1,X2,...,Xp0是1次齐次的,X0是2次齐次的.在本文中,我们研究如下带有漂移项的算子:L=∑p0i,j=1aijXiXj+a0X0,其中(aij)是一个常数矩阵且满足椭圆条件,a0∈R\{0}.对算子L,通过建立齐型空间上的奇异积分Morrey有界性和关于此向量场的插值不等式,我们在群G上获得了整体Sobolev-Morrey估计.

Abstract Let G be a homogeneous group and X0, X1, X2,..., Xpo be left invariant real vector fields on G satisfying the HSrmander＇s rank condition. Assume that X1, X2,..., Xpo are homogeneous of degree one and X0 is homogeneous of degree two. In this paper, we study the following hypoelliptic operator with drift： L=∑p0i,j=1aijXiXj＋a0X0 where （aij） is a constant matrie satisfying the uniform ellipticity condition and a0 is a constant away from zero, and obtain the global Sobolev-Morrey estimates on G by establishing the Morrey boundedness of the singular integrals on homogeneous spaces and interpolation inequalities depending on vector fields.