Global elliptic estimates on symmetric spaces

Abstract

The domination properties of elliptic invariant dierential operators on symmetric spaces of noncompact type are investigated. Using the relation between parametrices and fundamental solutions on symmetric space we will show that the invariant dierential operator applied to a function can be uniformly estimated by function and an elliptic operator of higher order applied to the function in Lp spaces for all 1 p 1. As a consequence, by algebraic methods we will give a simple unifying proof that derivatives of a function can be uniformly estimated by function and its Laplacian.