Subharmonic Functions, Generalizations, Holomorphic Functions, Meromorphic Functions, and Properties.

Subharmonic Functions, Generalizations, Holomorphic Functions, Meromorphic Functions, and Properties.

This book explains different types of subharmonic and harmonic functions. The book brings 12 chapters explaining general and specific types of subharmonic functions (eg. quasinearly subharmonic ...
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A mean value type inequality for quasinearly subharmonic functions

Pp. 30-36 (7)

DOI: 10.2174/9789811498701121010004

Author(s): Juhani Riihentaus

Abstract

Basing our proof on an old argument of Domar, we generalize and improve Armitage’s and Gardiner’s previous subharmonic function inequality result. Our result is stated for quasinearly subharmonic functions, it is rather general and, at the same time, flexible. Indeed, with the aid of it we will in the next two sections improve both Domar’s and our previous domination condition results of subharmonic functions, and also Armitage’s and Gardiner’s, and our results on the subharmonicity of separately subharmonic functions.

Keywords:

Subharmonic, quasinearly subharmonic, mean value, weighted integrals, control functions