, Volume 271, Issue 1, pp 179-198

Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators

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Abstract

We construct a continuous transition density of the semigroup generated by \({\Delta^{\alpha/2} + b(x)\cdot \nabla}\) for \({1 < \alpha < 2, d\ge 1}\) and b in the Kato class \({\mathcal{K}_d^{\alpha-1}}\) on \({\mathbb{R}^d}\) . For small time the transition density is comparable with that of the fractional Laplacian.

Communicated by B. Simon
Partially supported by KBN and MEN.