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| The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables* |
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Citation： |
Xiaosong LIU.The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables*[J].Chinese Annals of Mathematics B,2023,44(2):265~278 |
| Page view： 639
Net amount： 430 |
Authors： |
Xiaosong LIU; |
Foundation： |
National Natural Science Foundation of China (Nos. 11871257,12071130). |
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| Abstract： |
In this article, the refined Schwarz-Pick estimates for positive real part holomorphic functions p(x) = p(0) + ∞X m=kDmp(0)(xm)m!: G → C are given, where k is a positive integer, and G is a balanced domain in complex Banach paces. In particular, the results of first order Fr′echet derivative for the above functions and higher order Fr′echet derivatives for positive real part holomorphic functions p(x) = p(0) + ∞X s=1 Dskp(0)(x sk) (sk)! : G → C are sharp for G = B, where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces. Their results reduce to the classical result in one complex variable,and generalize some known results in several complex variables. |
Keywords： |
Refined Schwarz-Pick estimate, Positive real part holomorphic function,First order Fr´echet derivative, Higher order Fr´echet derivatives |
Classification： |
32A30, 32H02, 30C45 |
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