Chapter 6

Separately subharmonic and harmonic functions

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.

Total Pages: 56-67 (12)

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