## Abstract

We prove that uniform subellipticity of a positive symmetric second-order partial differential operator on L_{2}(R^{d}) is self-improving in the sense that it automatically extends to higher powers of the operator. The range of extension is governed by the degree of smoothness of the coefficients of the N operator. Secondly, if the operator is of the form X_{i} X_{i}, where the Xi are ^{N}∑ _{i=1}, vector fields on Rd with coefficients in C^{∞}_{b} (R^{d}) satisfying a uniform version of Hörmander's criterion for hypoellipticity, then we prove that it is uniformly subelliptic of order r^{-1}, where r is the rank of the set of vector fields.

Original language | English |
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Pages (from-to) | 125-149 |

Number of pages | 25 |

Journal | Journal of Operator Theory |

Volume | 62 |

Issue number | 1 |

Publication status | Published - Jun 2009 |