Potential Analysis

, Volume 34, Issue 1, pp 43–56

Some Weighted Energy Classes of Plurisubharmonic Functions

Article

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 Mχ. As an application, we prove a version of existence of solutions of Monge–Ampère type equations in the class \(\mathcal{E}_{\chi}(H,\Omega)\).

Keywords

Class \(\mathcal{E}_{\chi}\) Class \(\mathcal{E}\) Class \(\mathcal{N}\) Strong comparison principle Operator Mχ Monge–Ampère equation 

Mathematics Subject Classifications (2010)

32U05 32W20 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam

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