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 double-struck K sign;-bi-invariant kernels with certain large scale cancellation properties. As an application we prove Lp boundedness of operators defined by Fourier multipliers that satisfy singular differential inequalities of the Ho'rmander-Michlin type.
All Science Journal Classification (ASJC) codes
- Applied Mathematics