Singular integrals on symmetric spaces, II

Abstract

We extend some of our earlier results on boundedness of singular integrals on symmetric spaces of real rank one to arbitrary noncompact symmetric spaces. Our main theorem is a transference principle for operators defined by K \mathbb {K} -bi-invariant kernels with certain large scale cancellation properties. As an application we prove L p L^p boundedness of operators defined by Fourier multipliers that satisfy singular differential inequalities of the Hörmander–Michlin type.