Global Derivatives

Abstract

In the previous chapter we applied techniques of homogenization theory to derive global Gaussian bounds on the subelliptic semigroup kernel K. Once these bounds are established, one can use quite different techniques based on L₂-estimates to obtain global bounds on the derivatives of K. The nature of these bounds is sensitive to the direction of the derivatives and, in particular, the local and global singularities are usually quite different. The differences reflect the global geometry of the group.