Riteria For Plurigarmonicity Of M-Harmonic Functions

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 𝛥 ̃
𝑓 = 𝛥 ̃
𝑓𝛼 = 0(𝛼 ≠ 0, 𝛼 ≠ 1, 𝛼 ∈ ℝ) proved to f  z 
be a n -harmonic function. Moreover,
if the function is harmonic on the unit ball and 𝑓𝑚(𝑧) is M-harmonic, then it is proved that 𝑓𝑚(𝑧) is pluriharmonic. At the same
time, if the function is harmonic and M-harmonic in the polydisk 𝑈2 ⊂ 𝐶2, then it is proved that it is n-harmonic..