## Kodai Mathematical Journal

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

#### 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.

#### Article information

Source
Kodai Math. J. Volume 28, Number 2 (2005), 209-219.

Dates
First available in Project Euclid: 11 August 2005

http://projecteuclid.org/euclid.kmj/1123767003

Digital Object Identifier
doi:10.2996/kmj/1123767003

Mathematical Reviews number (MathSciNet)
MR2153910

Zentralblatt MATH identifier
1079.31002

#### Citation

Aikawa, Hiroaki; Lundh, Torbjörn. The 3G inequality for a uniformly John domain. Kodai Math. J. 28 (2005), no. 2, 209--219. doi:10.2996/kmj/1123767003. http://projecteuclid.org/euclid.kmj/1123767003.