On the Hölder continuity of weighted $m$-extremal functions

Kobiljon Kuldoshev^a, Karim Rakhimov<sup>b

a</sup> National University of Uzbekistan, Tashkent, Uzbekistan
^b V. I. Romanovskiy Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

Abstract: In this paper, we prove that if the weighted $m$-subharmonic measure of compact $K$ are Hölder continuous with respect to $K$, then it is Hölder continuous everywhere.

Keywords: $m$-subharmonic function, weighted $m$-Green function, weighted $m$-subharmonic measure.

UDC: 517.55

Received: 10.05.2025
Received in revised form: 30.06.2025
Accepted: 04.09.2025

Language: English