We 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...[Show more]
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|Source:||Journal of Operator Theory|
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