A_∞ and the Green function

Jang-Mei Gloria Wu

Vol. 157 (1993), No. 1, 159–178

DOI: 10.2140/pjm.1993.157.159

Abstract

Let G(x) be the Green function in a domain Ω ⊆ ℝ^m with a fixed pole, and Γ be an (m − 1)-dimensional hyperplane. We give conditions on Ω and Ω ∩ Γ so that |∇G| is A_∞ with respect to the (m − 1)-dimensional measure on Ω ∩ Γ. Certain properties of the Riemann mapping of a simply-connected domain in ℝ² are extended to the Green function of domains in ℝ^m.

Mathematical Subject Classification 2000

Primary: 31B05

Milestones

Received: 15 April 1991

Published: 1 January 1993