Intrinsic Hardy inequality for fractional Kolmogorov operator

TL;DR

This paper establishes a Hardy inequality for a non-local diffusion operator with a singular drift at a critical attraction strength, advancing understanding of fractional Kolmogorov operators.

Contribution

It introduces a Hardy inequality for fractional Kolmogorov operators with critical singular drift, a novel result in non-local diffusion analysis.

Findings

Hardy inequality proven for fractional Kolmogorov operator

Applicable at critical attraction strength

Enhances understanding of non-local diffusion with singular drift

Abstract

We obtain Hardy inequality for non-local diffusion operator with singular drift, in the case when the strength of attraction to the origin by the drift takes the critical value.