Global estimates in Sobolev spaces for homogeneous Hörmander sums of squares

Let L = ? j 1 m X 2 be a Hörmander sum of squares vector fields in space R n , where any is homogeneous degree with respect to family non-isotropic dilations space. In this paper we prove global estimates and regularity properties for the -Sobolev spaces W k p ( ) { … } . our approach, combine local results general sums squares, homogeneity property 's, plus lifting technique fields.