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| Mappings Which Have a Parametric Representation in Several Complex Variables |
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Citation： |
Xiaosong LIU,Taishun LIU.Mappings Which Have a Parametric Representation in Several Complex Variables[J].Chinese Annals of Mathematics B,2016,37(4):553~570 |
| Page view： 1830
Net amount： 1052 |
Authors： |
Xiaosong LIU; Taishun LIU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11031008, 11471111) and Guangdong Natural
Science Foundation (No.2014A030307016). |
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| Abstract： |
In this paper, the sharp distortion theorems of the
Fr\'echet-derivative type for a subclass of biholomorphic mappings
which have a parametric representation on the unit ball of complex
Banach spaces are established, and the corresponding results of the
above generalized mappings on the unit polydisk in $\mathbb{C}^n$
are also given. Meanwhile, the sharp distortion theorems of the
Jacobi determinant type for a subclass of biholomorphic mappings
which have a parametric representation on the unit ball with an
arbitrary norm in $\mathbb{C}^n$ are obtained, and the corresponding
results of the above generalized mappings on the unit polydisk in
$\mathbb{C}^n$ are got as well. Thus, some known results in prior
literatures are generalized. |
Keywords： |
Distortion theorem, A zero of order $k+1$, Fr\'echet-derivative,
Jacobi determinant, Parametric representation |
Classification： |
32A30, 32H02 |
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