Computational Methods and Function Theory 8 (2008), No. 1, 151--158
Copyright Heldermann Verlag 2008
Thomas Ransford
ransford@mat.ulaval.ca , Université Laval, Département de mathématiques et de statistique, Québec (QC), G1K 7P4, Canada.
Jérémie Rostand
jrostand@mat.ulaval.ca , Université Laval, Département de mathématiques et de statistique, Québec (QC), G1K 7P4, Canada.
We obtain improved estimates for the Hölder exponents of Green's functions associated to Cantor ternary sets. In particular, we show that the Green's function associated to the classical Cantor middle-third set is Hölder continuous of order at least $0.3413$.
Keywords: Green's function, Hölder continuity property, Cantor set.
MSC 2000: Primary 31A15; Secondary 30C85, 65E05.
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