关于C.Fefferman定理与全纯映射的边界扩充

On C. Fefferman's Theorem and Extendability of Holomorphic Mappings

C．Fefferman定理证明了光滑有界强拟凸域之间的双全纯映射可以光滑延拓到边幂,这个结果已经被推广到各种情形．其中Bell和Catlin[21]以及Diederich和Fornaess[44]独立地将其推广到拟凸域的逆紧全纯映射．本文较全面地综述了C．Fefferman定理的推广情况以及Bergman投射的边界正则性问题,同时对如何去掉Bell和Catlin[21]以及Diederich和Fbrnaess[44]定理条件中为拟凸性给出一个新观察,提出一个解决方向并且说明在具体情况下这个新观察确实是可以提供答案的．

C. Fefferman＇s theorem has shown that any biholomorphic mapping between smooth bounded domains can extend smoothly to the boundary. This result has been generalized to several cases. In particularly, Bell and Catlin^[21] and Diederieh and Fornaess%[44] generalized it to proper holomorphic mappings of pseudoconvex domains independently. This paper is a relatively complete survey about the generalizations of C. Fefferman＇s theorem and the boundary regularity of the Bergman projection. At the same time, a new observation is found on dropping the condition of pseudoconvexity in the theorem of Bell and Catlin^[21] and Diederieh and Fornaess^[44]. Furthermore, a solving way is presented and by some concrete examples the new observation is proved to be right and robust.