The Lusin-Privalov theorem for subharmonic functions

Author:

Gardiner Stephen

Abstract

This paper establishes a generalization of the Lusin-Privalov radial uniqueness theorem which applies to subharmonic functions in all dimensions. In particular, it answers a question of Rippon by showing that no subharmonic function on the upper half-space can have normal limit -\infty at every boundary point.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

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2. A asymptotic analog of the F. and M. Riesz radial uniqueness theorem;Barth, K. F.;Proc. Amer. Math. Soc.,1969

3. Analogues of radial uniqueness theorems for subharmonic functions in the unit disk;Berman, Robert D.;J. London Math. Soc. (2),1984

4. Cambridge Tracts in Mathematics and Mathematical Physics, No. 56;Collingwood, E. F.,1966

5. A characterization of Boolean algebras;Birkhoff, Garrett;Ann. of Math. (2),1939

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