首页|A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES
A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES
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In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞Σs=1Dskf(0)(xsk)/(sk)!:BX→BY,where Bx 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)+∞Σs=kDsf(0)(xs)/s!:BX → BY,where BX 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.
refined Schwarz-Pick estimatebounded holomorphic mappingCarathéodory metricfirst order Fréchet derivativehigher order Fréchet derivatives
刘小松、刘太顺
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School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,China
Department of Mathematics,Huzhou University,Huzhou 313000,China
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