Prof. Damir Kinzebulatov “Heat kernel of fractional Laplacian with Hardy drift via desingularizing weights”

I will discuss two-sided weighted bounds on the heat kernel of the
fractional Laplacian perturbed by a drift having critical-order
singularity. I will focus on the attracting case (the weights in the heat
kernel bounds “explode” at the singularity of the drift), but will also
discuss the repulsing case (the weights in the heat kernel bounds
vanish). The method consists of transferring the operator to an
appropriate weighted space, and then using some ideas of J. Nash.
That said, in this fractional setting the Dirichlet form approach
becomes problematic, so we pursue another point of view. In order to
carry out the calculations with the fractional Laplacian, we have to deal

with a rather subtle regularization of the singular weight.
This is a joint work with Yu.A.Semenov and K.Szczypkowski.