Robinson, Derekter Elst, A F M2015-12-080379-4024http://hdl.handle.net/1885/37568We prove that uniform subellipticity of a positive symmetric second-order partial differential operator on L2(Rd) 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 Xi Xi, where the Xi are N∑ i=1, vector fields on Rd with coefficients in C∞b (Rd) 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.Keywords: Double commutators; Hörmander sums of squares; Subelliptic operator20092016-02-24