多复变数函数的Schwarz引理

<正> §1.内容的简单介绍当试把Schwarz引理推广到多个复变数论者,曾有H.Cartan,Carathéo-dory,Bergmann,Bochner-Martin,Bureau,Фукс,Ozaki-Kashiwagi-Tsuboi,Sthr.但从这许多的前人之结果中,仍然使人产生一问题,就是Schwarz 引理能否推广与在什么意义下能推广.

SCHWARZ LEMMA IN THE THEORY OF FUNCTIONS OF SEVERAL COMPLEX VARIABLES

In this paper the author gives a complete and detailed proof of the re-sults announced in Science Record,New set.vol.Ⅰ.No.2(1957),6—9.Besides,there are generalizations and consequences of the previousresults,i.e.1°If a bounded schlicht domain D is transitive,there exists a posi-tive constant κ depending only on D such that for any bounded schlichtdomain D and any analytic mapping w=f(z)carrying D into D we al-ways have(?)2°If D is a bounded schlicht transitive domain and if there is al-ways a unique geodesic passing through any two points of D,then,for anytwo points z_1,z_2 ∈(?)and any inner analytic mapping carrying z_1,z to w_1,w_2 respectively,we always havewhere x(z_1,z_2)is the geodesic distance between z_1 and z_2,and κ_0(?)theSchwarz constant of D~(1)).3°If R is the topology product of the classical domains (?)~((1)),(?)~((2)),…,R~((j)),i.e.R=(?)~((1))×R~((2))×…×R~((j)),then the Schwarz constant ofR satisfies the relation(?)