Riteria For Plurigarmonicity Of M-Harmonic Functions

Abstract

It is proved in the paper that if a function f  z 
is M-harmonic in a polydisk
n U , then the function   2 f z
is Msubharmonic.
In addition, the case is ???? ̃
???? = ???? ̃
???????? = 0(???? ≠ 0, ???? ≠ 1, ???? ∈ ℝ) proved to f  z 
be a n -harmonic function. Moreover,
if the function is harmonic on the unit ball and ????????(????) is M-harmonic, then it is proved that ????????(????) is pluriharmonic. At the same
time, if the function is harmonic and M-harmonic in the polydisk ????2 ⊂ ????2, then it is proved that it is n-harmonic..