Green function estimate for censored stable processes

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Estimates and structure of α-harmonic functions (2006, background): “For more information on typical applications we refer the reader to [11], [30], [12], [20], [13], [14], [22], see also [25] for a general perspective.”
Nonlocal problems with Neumann boundary conditions (2014, background): “1 As we will see below, the corresponding heat equation with homogeneous Neumann conditions ut + (−∆) su = 0 in Ω, t > 0 Nsu = 0 in R n \ Ω, t > 0 u(x, 0) = u0(x) in Ω, t = 0 (1.4) possesses natural properties like conservation of mass inside Ω or convergence to a constant as t→ +∞ (see Section…”
Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “Accordingly, the Green function of smooth sets enjoys approximate factorization for rather general isotropic Lévy processes ([29, 66]).”
Two-sided heat kernel estimates for censored stable-like processes (2010, methodology): “We emphasize here that the Green function estimates for censored stable processes obtained in [4] will not be used in this paper.”
HARDY INEQUALITY FOR CENSORED STABLE PROCESSES (2003, methodology): “In [ 9 ], the Hardy inequality will be applied, together with the Harnack and boundary”