EMBEDDING-THEOREMS ON CAMPANATO-MORREY SPACES FOR VECTOR-FIELDS AND APPLICATIONS

We present some new embedding theorems on Campanato-Morrey spaces asso ciated with vector fields satisfying Hormander's condition. The main t heorem is [GRAPHICS] where X(1),...,X(m) are C-infinity vector fields of Hormander type. Unlike the Poincare inequality, such embedding theo rems allow larger, gaps than 1/Q, which is known to be true for the Po incare and Sobolev inequalities so far (see [10]). As applications, we will study the local regularity of solutions to subelliptic PDE with coefficients in appropriate Campanato-Morrey spaces.