  For $\alpha \in (1,2)$ we consider the equation $\partial_t u =
\Delta^{\alpha/2} u - r b \cdot \nabla u$, where $b$ is a divergence free
singular vector field not necessarily belonging to the Kato class. We show that
for sufficiently small $r>0$ the fundamental solution is globally in time
comparable with the density of the isotropic stable process

Probability