Lp Fourier multipliers on compact Lie groups
  In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem. 
Michael Ruzhansky and Jens Wirth
math.FA math.AP math.RT