Martin representation, Relative Fatou Theorem and Hardy spaces for fractional Laplacian with a gradient perturbation
Résumé
Let $L=\Delta^{\alpha/2}+ b\cdot\nabla$ with $\alpha\in(1,2)$. We prove several properties of singular $L$-harmonic functions on a ${\mathcal C}^{1,1}$ bounded open set $D$ : the Martin representation, the Relative Fatou Theorem and the representation theorem for Hardy spaces.
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