Critical heat kernel estimates for Schrodinger operators via Hardy-Sobolev inequalities

摘要

We obtain Sobolev inequalities for the Shcr6dinger operator -Delta-V, where V has critical behaviour V(x) = ((N - 2)/2)(2)x(-2) near the origin. We apply these inequalities to obtain point-wise estimates on the associated heat kernel, improving upon earlier results. (C) 2003 Elsevier Inc. All rights reserved. [References: 21]