Publications [#243472] of Richard T. Durrett

Papers Published

1. Chen, ZQ; Durrett, R; Ma, G, Holomorphic diffusions and boundary behavior of harmonic functions, Annals of Probability, vol. 25 no. 3 (January, 1997), pp. 1103-1134, Institute of Mathematical Statistics [doi]
   (last updated on 2024/04/18)

   Abstract:
   We study a family of differential operators {Lα, α ≥ 0} in the unit ball D of Cn with n ≥ 2 that generalize the classical Laplacian, α = 0, and the conformal Laplacian, α = 1/2 (that is, the Laplace-Beltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of Lα-harmonic functions is studied in a unified way for 0 ≤ α ≤ 1/2. More specifically, we show that a bounded Lα-harmonic function in D has boundary limits in approaching regions at almost every boundary point and the boundary approaching region increases from the Stolz cone to the Korányi admissible region as α runs from 0 to 1/2. A local version for this Fatou-type result is also established.