$$L^p$$Lp Fourier multipliers on compact Lie groups

@article{Ruzhansky2015LpLpFM,
  title={\$\$L^p\$\$Lp Fourier multipliers on compact Lie groups},
  author={Michael Ruzhansky and J. Wirth},
  journal={Mathematische Zeitschrift},
  year={2015},
  volume={280},
  pages={621-642}
}
In this paper we prove $$L^p$$Lp Fourier multiplier theorems for invariant and also non-invariant operators on compact Lie groups in the spirit of the well-known Hörmander–Mikhlin theorem on $$\mathbb R^n$$Rn and its variants on tori $$\mathbb T^n$$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. 
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