Math @ Duke

Publications [#243472] of Richard T. Durrett
Papers Published
 Chen, ZQ; Durrett, R; Ma, G, Holomorphic diffusions and boundary behavior of harmonic functions,
The Annals of Probability, vol. 25 no. 3
(January, 1997),
pp. 11031134, Institute of Mathematical Statistics [doi]
(last updated on 2019/04/24)
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 LaplaceBeltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of Lαharmonic functions is studied in a unified way for 0 ≤ α ≤ 1/2. More specifically, we show that a bounded Lαharmonic 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 Fatoutype result is also established.


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