Doubling Properties for Second Order Parabolic Equations in Memory of Eugene Fabes

We prove the doubling property of L-caloric measure corresponding to the second order parabolic equation in the whole space and in Lipschitz domains. For parabolic equations in the divergence form, a weaker form of the doubling property follows easily from a recent result, the backward Harnack inequality, and known estimates of the Green's function. Our method works for both the divergence and non-divergence cases. Moreover, the backward Harnack inequality and estimates of the Green's function are not needed in the course of proof.