On the Characterization of Harmonic and Subharmonic Functions via Mean-value Properties |
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| Authors: | Pedro Freitas João Palhoto Matos |
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| Institution: | 1.Department of Mathematics, Faculdade de Motricidade Humana (TU Lisbon) and Group of Mathematical Physics of the University of Lisbon,Complexo Interdisciplinar,Lisboa,Portugal;2.Departamento de Matemática,Instituto Superior Técnico,Lisboa,Portugal |
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| Abstract: | We consider the different characterizations of harmonic and subharmonic functions in terms of their mean values in balls and
on spheres. In particular, we prove a converse of an inequality of Beardon’s for subharmonic functions, and extend Rao’s integral
inequalities of Harnack type between these two means in general domains. |
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