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The Complex Monge–Ampère Operator on Bounded Domains in \({\mathbb{C}^{n}}\)

Abstract.

The aim of the present paper is to establish the inequality of Xing’s type for the class \({\mathcal{D}}\) introduced and investigated by [7] in recent time. Some properties of the class of \({\mathcal{D}}\) is given. The weak continuity of the Monge–Ampère on the class \({\mathcal{B}_{loc}}\) is considered. Finally we give some results on the range of the Monge–Ampère operator in the class \({\mathcal{D}^{u,a}}\) and \({\mathcal{B}^{u,a}_{loc}}\).

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Correspondence to Le Mau Hai.

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Received: June 12, 2007. Revised: September 21, 2008.

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Mau Hai, L., Van Khue, N. & Hoàng Hiệp, P. The Complex Monge–Ampère Operator on Bounded Domains in \({\mathbb{C}^{n}}\). Results. Math. 54, 309–328 (2009). https://doi.org/10.1007/s00025-009-0360-6

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  • DOI: https://doi.org/10.1007/s00025-009-0360-6

Mathematics Subject Classification (2000).

  • Primary 32U05
  • Secondary 32U40

Keywords.

  • The complex Monge–Ampère operator
  • bounded domains
  • the class \({\mathcal{D}}\)
  • comparison principle