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Subharmonic functions inn-connected domains

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
153
Issue
1
Identifiers
DOI: 10.1016/0022-247x(90)90260-m

Abstract

Abstract In this paper we investigate some of the properties of harmonic and subharmonic functions defined on n-connected domain G. In particular, we study the behavior of subharmonic functions at every point of the boundary of G. We prove that if f is subharmonic and u f is the least harmonic majorant of f then the lim sup taken along the normal to the boundary of G of f(z) P(z, x) converges to the singular part of the boundary measure of u f evaluated at x. The result is true for every x belonging to the boundary of G.

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