A GLOBAL LOWER-BOUND FOR THE FUNDAMENTAL SOLUTION OF KOLMOGOROV-FOKKER-PLANCK EQUATIONS

The main result of this paper is a global lower bound for the fundamen tal solution Gamma of the ultraparabolic differential operator [GRAPHI CS] where the a(i),(j)'s and their first derivatives are Holder contin uous functions and 0 < p(0) < N. The bound will follow from a local es timate of Gamma and a Harnack inequality for non-negative solutions of Lu = 0, by exploiting the invariance of the Harnack inequality with r espect to suitable translation and dilation groups. For non-degenerate parabolic operators, our methods and results generalize those of ARON SON & SERRIN [1].