TY - JOUR
T1 - Positive superharmonic functions and the Hölder continuity of conformal mappings
AU - Anderson, J. M.
AU - Hinkkanen, A.
PY - 1989/4
Y1 - 1989/4
N2 - We study the rate at which a positive superharmonic function u can tend to zero at a boundary point z
0of a plane domain G. In particular, if G is a quasidisk, and a > 0 is given, we show that the condition that lim inf «(z)/dist (z, dG)
llct> 0 as z -* z
0in G for any such u is related to the condition that the conformal map/of the unit disk onto G withal) = z
0is Holder continuous with exponent a at the point 1. This leads us to consider the problem of finding the best exponent a for which /is Holder continuous. The answer depends on how we characterize quasidisks or quasicircles. In this connection we give a negative answer to a question of Nakki and Palka.
AB - We study the rate at which a positive superharmonic function u can tend to zero at a boundary point z
0of a plane domain G. In particular, if G is a quasidisk, and a > 0 is given, we show that the condition that lim inf «(z)/dist (z, dG)
llct> 0 as z -* z
0in G for any such u is related to the condition that the conformal map/of the unit disk onto G withal) = z
0is Holder continuous with exponent a at the point 1. This leads us to consider the problem of finding the best exponent a for which /is Holder continuous. The answer depends on how we characterize quasidisks or quasicircles. In this connection we give a negative answer to a question of Nakki and Palka.
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U2 - 10.1112/jlms/s2-39.2.256
DO - 10.1112/jlms/s2-39.2.256
M3 - Article
SN - 0024-6107
VL - s2-39
SP - 256
EP - 270
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 2
ER -