On a martingale method for symmetric diffusion processes and its applications

a martingale method for symmetric diffusion processes andits application

OPTIMAL HARDY-TYPE INEQUALITIES FOR SCHRÖDINGER FORMS

We give a method to construct a critical Schrödinger form from the subcritical Schrödinger form by subtracting a suitable positive potential. The method enables us to obtain optimal Hardy-type inequalities

Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms

Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general perturbed divergence form operators. Our main tool is a recently extended forward and backward martingale decomposition, which reduces to the well-known Lyons-Zheng decomposition in the symmetric case.Comment: Corrected typos, minor modification