Critical heat kernel estimates via Hardy-Sobolev inequalities
arXiv:math/0302331
Abstract
We obtain Sobolev inequalities for the Schrodinger operator -Δ-V, where V has critical behaviour V(x)=((N-2)/2)^2|x|^{-2} near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel, improving upon earlier results.
23 pages