The Schwarz Lemma At The Boundary Of The Generalized Complex Ellipsoid In C~n

For the generalized complex ellipsoid BP1,P2 = {z ∈Cn:|Z1|p1+（|z2|2 + …+{zn}2）p2<1}（Pi≥ 1,P2 ≥1）in Cn,we establish a new type of boundary Schwarz lemma for holomorphic self-mappings of Bp11,P2 in this paper.This paper consists of three parts,the first part introduces the background and outlines of our research result for Schwarz lemma at the boundary of a generalized complex ellipsoid;and the second part gives the preliminary knowledge of the Schwarz lemma at the boundary and the complex ellipsoids,such as the definitions and properties of the Caratheodory pseudometric and Kobayashi pseudometric and the Minikowski functional,and so on;the last part gives the proof of our main theorem the Schwarz lemma at some boundary points of the generalized complex ellipsoid B_p1,p2.