Potential Analysis

, Volume 34, Issue 1, pp 43–56

Some Weighted Energy Classes of Plurisubharmonic Functions


DOI: 10.1007/s11118-010-9179-8

Cite this article as:
Hai, L.M. & Hiep, P.H. Potential Anal (2011) 34: 43. doi:10.1007/s11118-010-9179-8


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 \(\mathcal{E}_{\chi}(H,\Omega)\).


Class \(\mathcal{E}_{\chi}\)Class \(\mathcal{E}\)Class \(\mathcal{N}\)Strong comparison principleOperator MχMonge–Ampère equation

Mathematics Subject Classifications (2010)


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam