SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN
Zhangyiping · Acta Scientiarum Naturalium Universitatis Sunyatseni · 1996
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 exanlples are given.