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Jensen measures and unbounded B - regular domains in C n

Quang Dieu Nguyen;  Dau Hoang Hung — 2008

Annales de l’institut Fourier

Following Sibony, we say that a bounded domain Ω in C n is B -regular if every continuous real valued function on the boundary of Ω can be extended continuously to a plurisubharmonic function on Ω . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in C n . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work

B-regularity of certain domains in ℂⁿ

Nguyen Quang Dieu;  Nguyen Thac Dung;  Dau Hoang Hung — 2005

Annales Polonici Mathematici

We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.

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