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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Separately subharmonic and harmonic functions

Pp. 56-67 (12)

DOI: 10.2174/9789811498701121010007

Author(s): Juhani Riihentaus

Abstract

It is an open problem whether a function, subharmonic with respect to the first variable and harmonic with respect to the second, is subharmonic or not. Based again on our mean value type inequality, we improve our previous subharmonicity results of the above type functions, thus improving also the previous results of Kołodziej and Thorbiörnson and Imomkulov. Moreover, we give refinements, with concise proofs, to the older basic results of Arsove, and of Cegrell and Sadullaev.

Keywords:

Subharmonic, quasinearly subharmonic, separately quasinearly subharmonic and harmonic