This article is cited in 1 paper

Delta-extremal functions in $\mathbb{C}^n$

Nurbek Kh. Narzillaev

National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: The article is devoted to properties of a weighted Green function. We study the $(\delta,\psi)$-extremal Green function $V^{*}_{\delta}(z,K,\psi)$ defined by the class $\mathcal{L}_{\delta}=\big\{u(z)\in psh(\mathbb C^{n}):\ u(z) \leqslant C_{u}+\delta\ln^{+}|z|, \ z\in\mathbb C^{n}\big\}, \ \delta>0.$ We see that the notion of regularity of points with respect to different numbers $\delta$ differ from each other. Nevertheless, we prove that if a compact set $K\subset\mathbb{C}^{n}$ is regular, then $\delta$-extremal function is continuous in the whole space $\mathbb C^{n}.$

Keywords: plurisubharmonic function, Green function, weighted Green function, $\delta$-extremal function.

UDC: 517.55

Received: 28.01.2021
Received in revised form: 01.03.2021
Accepted: 25.04.2021

Language: English

DOI: 10.17516/1997-1397-2021-14-3-389-398

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