## Abstract

This paper aims to prove a Hörmander multiplier theorem for sub-Laplacians on nilpotent Lie groups. We investigate the holomorphic functional calculus of the sub-Laplacians, then we link the L^{1} norm of the complex time heat kernels with the order of differentiability needed in the Hörmander multiplier theorem. As applications, we show that order d/2 + 1 suffices for homogeneous nilpotent groups of homogeneous dimension d, while for generalised Heisenberg groups with underlying space R^{2n+k} and homogeneous dimension 2n + 2k, we show that order n + (k + 5)/2 for k odd and n + 3 + k/2 for k even is enough; this is strictly less than half of the homogeneous dimension when k is sufficiently large.

Original language | English |
---|---|

Pages (from-to) | 413-424 |

Number of pages | 12 |

Journal | Pacific Journal of Mathematics |

Volume | 173 |

Issue number | 2 |

Publication status | Published - Apr 1996 |