Let be the basis of space of horizontal vector fields in a Carnot group . We prove high order Fefferman-Phong type inequalities in . As applications, we derive a priori estimates for the nondivergence degenerate elliptic operators with coefficients and a potential belonging to an appropriate Stummel type class introduced in this paper. Some of our results are also new even for the usual Euclidean space.
Pengcheng Niu. Kelei Zhang. "High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/274859