Harnack inequality for stable processes on d-sets

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Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “1) holds for some r0 (if X is unbounded, then it was proved in [27] that we can take r0 =∞).”
Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators (2007, background): “The estimate is well-known, and proved, e.g., in [ 8 ].”
Estimates and structure of α-harmonic functions (2006, result): “Our theorems complete and extend in several directions part of the results of [9,10,15,21,32,36,41].”
On Kelvin Transformation (2006, methodology): “For λ> 0 and every α∈ (0,2) by (12) and (14) we have”
Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, methodology): “We note that D is ((2 √ 1 + λ2)−1, r)-fat for all r > 0 ([16], Remark 1).”