Published September 25, 2024 | Version v1
Journal article Open

Riteria For Plurigarmonicity Of M-Harmonic Functions

  • 1. Tashkent State Pedagogical University,

Description

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 π›₯ Μƒ
𝑓 = π›₯ Μƒ
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 π‘“π‘š(𝑧) is M-harmonic, then it is proved that π‘“π‘š(𝑧) is pluriharmonic. At the same
time, if the function is harmonic and M-harmonic in the polydisk π‘ˆ2 ⊂ 𝐢2, then it is proved that it is n-harmonic..

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