The Estimates of All Homogeneous Expansions for a Subclass of Biholomorphic Mappings Which Have Parametric Representation in Several Complex Variables

In this paper, we obtain the estimates of all homogeneous expansions for a subclass of bi- holomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 33; no. 2; pp. 287 - 300
Main Authors Liu, Xiao Song, Liu, Tai Shun
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.02.2017
Springer Nature B.V
Subjects
Banach space
Banach spaces
Complex variables
Estimates
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Representations
Studies
starlike mapping
quasi-convex mapping
quasi-convex mapping of type A
starlike mapping of order
32A30
Estimate of homogeneous expansion
32H02
parametric representation
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Summary:In this paper, we obtain the estimates of all homogeneous expansions for a subclass of bi- holomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.
Bibliography:Estimate of homogeneous expansion, starlike mapping, starlike mapping of order α, quasi-convex mapping, quasi-convex mapping of type A, parametric representation
11-2039/O1
In this paper, we obtain the estimates of all homogeneous expansions for a subclass of bi- holomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5226-8