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Let $L=\Delta^{\alpha/2}+ b\cdot\nabla$ with $\alpha\in(1,2)$. We prove theMartin representation and the Relative Fatou Theorem for non-negative singular$L$-harmonic functions on ${\mathcal C}^{1,1}$ bounded open sets.

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