L^p-multipliers for Noncompact Symmetric Spaces

Abstract

Let G be a real noncompact semi-simple Lie group with finite center and K a maximal compact sub-group. The symmetric space M = G/K carries a measure invariant under the action of G. The operators which map L^p(M) continuously into itself and commute with the action of G, can be easily characterized when p = 2 or p = 1. This note gives some results on “singular integrals” which map L^p into itself (1 < p < + ∞).

• semi-simple Lie group
• maximal function
• singular integral operator