## Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

#### Article Title

### Weighted (m, δ)-green functions in C^{n}

#### Abstract

In this work some extremal function and its properties are studied for the class of *m*-subharmonic functions. We study weighted (*m*,*δ*)-Green function *V*_{m}^{*}(*z*,*K*,*ψ*,*δ*), defined by the class ℒ_{m}^{δ} = {*u*(*z*)∈*s**h*_{m}(ℂ^{n}): *u*(*z*)≤*δ*, *z*∈ℂ^{n}}, *δ* > 0. We see that the regularity of the points with respect to different numbers *δ* differ from each other. Nevertheless, we will prove that if the compact *K* ⊂ ℂ^{n} is (*m*,*δ*,*ψ*)-regular, then weighted (*m*,*δ*)-Green function is continuous in the whole space ℂ^{n}.

#### First Page

173

#### Last Page

184

#### References

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#### Recommended Citation

Narzillaev, Nurbek
(2021)
"Weighted (m, δ)-green functions in C^{n},"
*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*: Vol. 4:
Iss.
3, Article 4.

DOI: https://doi.org/10.56017/2181-1318.1198