Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Piotr Graczyk, Tomasz Jakubowski, Tomasz Luks

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}^…