Besov Estimates for Sub-elliptic Equations in the Heisenberg Group

Abstract: In this paper, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderon-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderon-Zygmund theory in the Heisenberg group.