Weighted (m, δ)-green functions in Cⁿ

Authors

Nurbek Narzillaev, National University of Uzbekistan, Tashkent, UzbekistanFollow

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)∈sh_m(ℂⁿ): u(z)≤δ, z∈ℂⁿ}, 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 ⊂ ℂⁿ is (m,δ,ψ)-regular, then weighted (m,δ)-Green function is continuous in the whole space ℂⁿ.

First Page

173

Last Page

184

References

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Recommended Citation

Narzillaev, Nurbek (2021) "Weighted (m, δ)-green functions in Cⁿ," 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