tailieunhanh - Báo cáo toán học: "A Remark on the Dirichlet Problem"

Cho một μ biện pháp tích cực trên một miền mạnh mẽ pseudoconvex Cn. Chúng tôi nghiên cứu vấn đề Dirichlet (DDC u) n = μ trong một lớp mới của chức năng plurisubharmonic. Lớp này bao gồm Ep các lớp học (p ≥ 1) được giới thiệu bởi Cegrell trong [5].1. | Vietnam Journal of Mathematics 33 3 2005 335-342 V Í e It ini ai m J o mt r im ai I of MATHEMATICS VAST 2005 A Remark on the Dirichlet Problem Pham Hoang Hiep Department of Mathematics Hanoi University of Education 136 Xuan Thuy Street Cau Giay Hanoi Vietnam Received October 06 2004 Revised March 03 2005 Abstract. Given a positive measure on a strongly pseudoconvex domain in C . We study the Dirichlet problem in a new class of plurisubharmonic function. This class includes the classes . introduced by Cegrell in 5 . 1. Introduction. .C. . . . . . . . . . . . . . . . . . .a. . This work was supported by the National Research Program for Natural Science Vietnam 336 Pham Hoang Hiep Main theorem. Let be a bounded strongly pseudoconvex domain in C and let be a positive measure on .such that there exists . B resp. . . with Then there exists . B a c resp. . a c such that and. There exists such that there exists no function . a . which satisfying. . a. . a. . . . 2. Preliminaries . . . . . . . . a. a. . . . . . . . . B j 1 A Remark on the Dirichlet Problem 337 . . . . . E. Theorem . The class has the following properties is a convex cone. . . . is weakly convergent. Conversely . satisfies and 3 then .-. . . . . . . . . . . . . . .