RUS  ENG
Full version
JOURNALS // Journal of Siberian Federal University. Mathematics & Physics // Archive

J. Sib. Fed. Univ. Math. Phys., 2025 Volume 18, Issue 3, Pages 387–401 (Mi jsfu1254)

$m-cv$ measure $\omega ^{*} (x,E,D)$ and condenser capacity $C(E,D)$ in the class $m$-convex functions

Azimbay Sadullaevab, Rasulbek Sharipovc, Mukhiddin Ismoilovb

a V. I. Romanovsky Institute of Mathematics, of the Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
b National University of Uzbekistan, Tashkent, Uzbekistan
c Urgench State University, Urgench, Uzbekistan

Abstract: In this work we study very basic concepts of potential theory: polar sets and $m-cv$ measures in the class of $m$-convex functions in real space ${\mathbb R}^{n}$. We also study capacity of condenser $C(E,D)$ in the class $m$-convex functions and will prove a number of its potential properties.

Keywords: $m$-subharmonic function, convex function, $m$-convex function, $m-cv$ polar set, $m-cv$ measure, Borel measures, Hessians.

UDC: 517.55+517.51

Received: 10.08.2024
Received in revised form: 15.09.2024
Accepted: 24.10.2024

Language: English



© Steklov Math. Inst. of RAS, 2025