Local property of the class \(\mathcal E_{\chi}, loc\) (Q1947305)

This paper is concerned with local properties of the classes of plurisubharmonic functions with finite weigthed energy in bounded hyperconvex domains in \(\mathbb C^n\) introduced by \textit{S. Benelkourchi} et al. [in: Complex analysis and digital geometry. Proceedings from the Kiselmanfest, Uppsala, Sweden, 2006, on the occasion of Christer Kiselman's retirement. Uppsala: Univ. Uppsala. 57--74 (2009; Zbl 1200.32021)]. These classes are related to the definition of the complex Monge-Ampère operator discovered by \textit{U. Cegrell} [Acta Math. 180, No. 2, 187--217 (1998; Zbl 0926.32042)]. In this paper the authors introduce local versions of the weighted energy classes and investigate their properties depending on the growth properties of the weights.