Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities

In the present paper we prove upper and lower bounds of the heat kernel for the operator Delta - del(vertical bar x vertical bar(-alpha) ) . del in R-n \ {0} where alpha > 0. We obtain these bounds from an isoperimetric inequality for a measure e(-vertical bar x vertical bar-alpha) dx on R-n \ {0}. The latter amounts to a certain functional isoperimetric inequality for the radial part of this measure.