Communications in Mathematical Physics

, Volume 271, Issue 1, pp 179–198

Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators


DOI: 10.1007/s00220-006-0178-y

Cite this article as:
Bogdan, K. & Jakubowski, T. Commun. Math. Phys. (2007) 271: 179. doi:10.1007/s00220-006-0178-y


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.

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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland