|
|
| |
| SOME BOUNDARY INCREASING PROPERTIES OFHARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN |
| |
Citation： |
Zhang Yiping.SOME BOUNDARY INCREASING PROPERTIES OFHARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN[J].Chinese Annals of Mathematics B,1996,17(2):159~166 |
| Page view： 0
Net amount： 620 |
Authors： |
Zhang Yiping; |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
|
|
| Abstract： |
The object of this paper is to study the non-tangential increasing properties
of positive harmonic function $u$ in Lipschitz domain by means of Martin
representation theory. A necessary and sufficient condition of
the control of growth of $u$ near any fixed boundary point is obtained.
It is shown that the non-tangential
increasing degree of $u$ near a boundary point is exactly the local
degree of its
representation measure with respect to the harmonic measure. Some examples
are given. |
Keywords： |
Martin representation, Harmonic function, Harmonic
measure |
Classification： |
31B25, 31C35 |
|
|
Download PDF Full-Text
|
