Martin representation and Relative Fatou Theorem for fractional   Laplacian with a gradient perturbation
  Let $L=\Delta^{\alpha/2}+ b\cdot\nabla$ with $\alpha\in(1,2)$. We prove the Martin representation and the Relative Fatou Theorem for non-negative singular $L$-harmonic functions on ${\mathcal C}^{1,1}$ bounded open sets. 
Piotr Graczyk, Tomasz Jakubowski, Tomasz Luks
math.AP