A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES  

作　　者：Xiaosong LIU Taishun LIU 刘小松;刘太顺(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,China;Department of Mathematics,Huzhou University,Huzhou 313000,China)

机构地区：[1]School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,China [2]Department of Mathematics,Huzhou University,Huzhou 313000,China

出　　处：《Acta Mathematica Scientia》2024年第4期1337-1346,共10页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(11871257,12071130);supported by the NSFC(11971165)。

摘　　要：In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

关 键 词：refined Schwarz-Pick estimate bounded holomorphic mapping Carathéodory metric first order Fréchet derivative higher order Fréchet derivatives 

分 类 号：O174.5[理学—数学]