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- W2006953612 abstract "In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in a bounded κ-fat open set; if u is a positive harmonic function with respect to X in a bounded κ-fat open set D and h is a positive harmonic function in D vanishing on Dc, then the non-tangential limit of u/h exists almost everywhere with respect to the Martin-representing measure of h." @default.
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- W2006953612 date "2013-02-01" @default.
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- W2006953612 title "Oscillation of harmonic functions for subordinate Brownian motion and its applications" @default.
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- W2006953612 doi "https://doi.org/10.1016/j.spa.2012.09.015" @default.
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