Kobiljon Kuldoshev | Searcharxiv

arXiv2026

Weighted $α$-subharmonic measure

In this paper, we introduce and study the weighted $α$-subharmonic measure associated with a weight function $ψ$, extending the usual $α$-subharmonic measure and reducing to it when $ψ\equiv -1$. Furthermore, we study the relationship between the weighted $α$-subharmonic measure and $α$-regular compact sets. We also obtain a characterization of $(α,ψ)$-regularity in terms of the continuity of the corresponding weighted $α$-subharmonic measure. Finally, we prove that if the weighted $α$-subharmonic measure of the compact set $K$ is Hölder continuous with respect to $K$, then it is Hölder continuous everywhere.

math.CV↗

arXiv2025

$(m, ψ, δ)-$capacity and its properties

In this paper, we introduce the concept of the generalized $(m, ψ, δ)-$capacity in the complex space $\mathbb{C}^n$, within the class of $m-$subharmonic functions. We give a relation between $(m, ψ, δ)-$capacity and $(m, ψ, δ)-$subharmonic measure. Moreover, we prove that the capacity vanishes on $m-$polar sets and vice versa.

math.CV↗