Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Article Title

Weighted (m, δ)-green functions in Cn


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 Vm*(z,K,ψ,δ), defined by the class ℒmδ = {u(z)∈shm(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.