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We construct the fundamental solutions for the sub-elliptic oper- ators in non-divergence form P i;jai;j(x;t)XiXj @t and P i;jai;j (x)XiXj, where the Xi's form a stratied system of Hormander vector elds and ai;j are Holder continuous functions belonging to a suitable class of ellipticity.

Levi’s parametrix for some sub-elliptic non-divergence form operators