Potential Analysis

, Volume 34, Issue 1, pp 43–56

Some Weighted Energy Classes of Plurisubharmonic Functions

Authors

    • Department of MathematicsHanoi National University of Education
  • Pham Hoang Hiep
    • Department of MathematicsHanoi National University of Education
Article

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

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 principleOperator MχMonge–Ampère equation

Mathematics Subject Classifications (2010)

32U0532W20

Copyright information

© Springer Science+Business Media B.V. 2010