The 3G inequality for a uniformly John domain
Aikawa, Hiroaki ; Lundh, Torbjörn
Kodai Math. J., Tome 28 (2005) no. 1, p. 209-219 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let G be the Green function for a domain D $\subset$ Rd with d ≥ 3. The Martin boundary of D and the 3G inequality: ¶ $\frac{G(x,y)G(y,z)}{G(x,z)} \le A(|x-y|^{2-d}+|y-z|^{2-d})$ for x,y,z $\in$ 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.
Publié le : 2005-06-14
Classification:  
@article{1123767003,
     author = {Aikawa, Hiroaki and Lundh, Torbj\"orn},
     title = {The 3G inequality for a uniformly John domain},
     journal = {Kodai Math. J.},
     volume = {28},
     number = {1},
     year = {2005},
     pages = { 209-219},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1123767003}
}

Aikawa, Hiroaki; Lundh, Torbjörn. The 3G inequality for a uniformly John domain. Kodai Math. J., Tome 28 (2005) no. 1, pp.  209-219. http://gdmltest.u-ga.fr/item/1123767003/