Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions

By M. Rao, Renming Song, Zoran Vondraček. 2006

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Citations in the corpus

Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, unknown): “Regarding other recent estimates [20, 17, 36, 23, 3] for the transition density and potential kernel of jump-type processes, we need to point out that generally these only concern processes without killing.”
Differentiability of spectral functions for symmetric $\alpha$-stable processes (2007, background): “Recently, Rao, Song and Vondraček [32] obtained asymptotic behaviors of Green functions of Lévy processes including relativistic α-stable processes.”
Potential Theory of Subordinate Brownian Motion (2009, background): “The materials covered in these lecture notes are based on several recent papers, primarily [47], [52], [59] and [57].”
Harnack inequalities for subordinate Brownian motions (2012, background): “2 in [15], (2.”
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian (2005, methodology): “That (2) implies (1) is proved by using a maximum principle for a Dynkin-type version of the operator A to explicitly estimate its Green function G(x, v) for the unit ball, see Proposition 1 below.”
Boundary Harnack principle for subordinate Brownian motions (2007, background): “3 of [21] we know that the potential measure U of S defined by U (A) := E ∫ ∞”
Potential theory of subordinate Brownian motions revisited (2011, background): “A lot of progress has been made in recent years in the study of the potential theory of subordinate Brownian motions, see, for instance [13, 14, 25, 26, 27, 31, 35] and [6, Chapter 5].”