Heat kernel of fractional Laplacian with Hardy drift via desingularizing weights

TL;DR

This paper derives precise bounds for the heat kernel of a fractional Laplacian with a Hardy-type drift by employing weighted spaces to manage singularities, advancing understanding of such operators.

Contribution

It introduces a novel approach using weighted spaces to handle critical singularities in the heat kernel of fractional Laplacians with Hardy drift.

Findings

Established sharp two-sided bounds on the heat kernel.

Successfully managed critical singularities via weighted space techniques.

Enhanced theoretical understanding of fractional Laplacian operators with singular drifts.

Abstract

We establish sharp two-sided bounds on the heat kernel of the fractional Laplacian, perturbed by a drift having critical-order singularity, by transferring it to appropriate weighted space with singular weight.