Published September 25, 2024
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Riteria For Plurigarmonicity Of M-Harmonic Functions
- 1. Tashkent State Pedagogical University,
Description
It is proved in the paper that if a function f ο¨ z ο©
is M-harmonic in a polydisk
n U , then the function ο¨ ο© 2 f z
is Msubharmonic.
In addition, the case is π₯ Μ
π = π₯ Μ
ππΌ = 0(πΌ ≠ 0, πΌ ≠ 1, πΌ ∈ β) proved to f ο¨ z ο©
be a n -harmonic function. Moreover,
if the function is harmonic on the unit ball and ππ(π§) is M-harmonic, then it is proved that ππ(π§) is pluriharmonic. At the same
time, if the function is harmonic and M-harmonic in the polydisk π2 ⊂ πΆ2, then it is proved that it is n-harmonic..
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