Article

Potential Analysis

, Volume 34, Issue 1, pp 43-56

Some Weighted Energy Classes of Plurisubharmonic Functions

  • Le Mau HaiAffiliated withDepartment of Mathematics, Hanoi National University of Education Email author 
  • , Pham Hoang HiepAffiliated withDepartment of Mathematics, Hanoi National University of Education

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

Keywords

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

Mathematics Subject Classifications (2010)

32U05 32W20