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 \(\mathcal{E}_{\chi}(H,\Omega)\).
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Hai, L.M., Hiep, P.H. Some Weighted Energy Classes of Plurisubharmonic Functions. Potential Anal 34, 43–56 (2011). https://doi.org/10.1007/s11118-010-9179-8
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DOI: https://doi.org/10.1007/s11118-010-9179-8
Keywords
- Class \(\mathcal{E}_{\chi}\)
- Class \(\mathcal{E}\)
- Class \(\mathcal{N}\)
- Strong comparison principle
- Operator M χ
- Monge–Ampère equation