M ar 2 00 5 On Hessian measures for non - commuting vector fields
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چکیده
Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L 1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, 1 ≤ k ≤ m.
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Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L 1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, 1 ≤ k ≤ m.
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تاریخ انتشار 2005