previous :: next

### The 3G inequality for a uniformly John domain

Hiroaki Aikawa and Torbjörn Lundh
Source: Kodai Math. J. Volume 28, Number 2 (2005), 209-219.

#### Abstract

Let G be the Green function for a domain D Rd with d ≥ 3. The Martin boundary of D and the 3G inequality:

for x,y,z D

are studied. We give the 3G inequality for a bounded uniformly John domain D, although the Martin boundary of D need not coincide with the Euclidean boundary. On the other hand, we construct a bounded domain such that the Martin boundary coincides with the Euclidean boundary and yet the 3G inequality does not hold.

First Page:
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.kmj/1123767003
Digital Object Identifier: doi:10.2996/kmj/1123767003
Zentralblatt MATH identifier: 1079.31002
Mathematical Reviews number (MathSciNet): MR2153910

previous :: next