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Results in Mathematics

, Volume 54, Issue 3–4, pp 309–328 | Cite as

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

  • Le Mau HaiEmail author
  • Nguyen Van Khue
  • Phạm Hoàng Hiệp
Article
  • 78 Downloads

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 \({\mathcal{B}^{u,a}_{loc}}\).

Mathematics Subject Classification (2000).

Primary 32U05 Secondary 32U40 

Keywords.

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

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Le Mau Hai
    • 1
    Email author
  • Nguyen Van Khue
    • 1
  • Phạm Hoàng Hiệp
    • 1
  1. 1.Department of MathematicsHa Noi National University of EducationHa NoiViet Nam

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