, Volume 34, Issue 1, pp 43-56
Date: 22 Apr 2010

Some Weighted Energy Classes of Plurisubharmonic Functions

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Abstract

In this paper we study relations between the weighted energy class \(\mathcal{E}_{\chi}\) introduced by S. Benelkourchi, V. Guedj and A. Zeriahi recently with Cegrell’s classes \(\mathcal{E}\) and \(\mathcal{N}\) . Next we establish a generalized comparison principle for the operator M χ . As an application, we prove a version of existence of solutions of Monge–Ampère type equations in the class \(\mathcal{E}_{\chi}(H,\Omega)\) .