Characterization of harmonic and subharmonic functions via mean-value properties

Details Characterization of harmonic and subharmonic functions via mean-value properties Characterization of harmonic and subharmonic functions via mean-value properties

2001-06-11

arxiv.org/abs/math/0106078v1

Mathematics

Analysis of PDEs

9 pages

Scientific paper

We give a characterization of harmonic and subharmonic functions in terms of
their mean values in balls and on spheres. This includes the converse of an
inequality of Beardon's for subharmonic functions. We also obtain integral
inequalities of Harnack type between these two means in general domains.

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