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.
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)
基金
supported by the NSFC(11871257,12071130)
supported by the NSFC(11971165)。
