THE PARAMETRIC REPRESENTATION FOR SPIRAL-LIKE MAPPINGS OF TYPE α ON BOUNDED BALANCED PSEUDOCONVEX DOMAINS
Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a spiral-like mapping of type a on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-li...
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| Published in | Acta Mathematica Scientia Vol. 26; no. 3; pp. 421 - 430 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.07.2006
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 1003-3998 |
| DOI | 10.1016/S0252-9602(06)60066-0 |
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| Abstract | Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a spiral-like mapping of type a on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up. |
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| AbstractList | Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a spiral-like mapping of type a on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up. O4; Let Ω be a bounded balanced pseudoconvex domain in Cn that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a spiral-like mapping of type α on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up. Let Omega be a bounded balanced pseudoconvex domain in n that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a spiral-like mapping of type alpha on Omega, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type alpha are obtained. As a direct application, the growth theorem for spiral-like mappings of type alpha is set up. |
| Author | 刘浩 张志平 卢克平 |
| AuthorAffiliation | Institute of Mathematics and information science, Henan University, Kaifeng 475001, China |
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| Cites_doi | 10.1016/S0252-9602(17)30316-8 10.1007/BF01344545 10.1080/17476939908815195 10.1090/conm/142/1208782 10.1007/BFb0096834 |
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| Keywords | growth theorem Spiral-like mappings parametric representation |
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| References | Hua (10.1016/S0252-9602(06)60066-0_bib4) 1963 Hamada (10.1016/S0252-9602(06)60066-0_bib9) 1999; 39 Jin (10.1016/S0252-9602(06)60066-0_bib10) 1962 Feng (10.1016/S0252-9602(06)60066-0_bib14) 2002; 22B Suffridge (10.1016/S0252-9602(06)60066-0_bib7) 1977 Dieudonne (10.1016/S0252-9602(06)60066-0_bib12) 1960 Shi (10.1016/S0252-9602(06)60066-0_bib13) 1996 Gong (10.1016/S0252-9602(06)60066-0_bib3) 1999 Pfaltzgraff (10.1016/S0252-9602(06)60066-0_bib8) 1974; 210 Gong (10.1016/S0252-9602(06)60066-0_bib2) 1993; 142 Gurganus (10.1016/S0252-9602(06)60066-0_bib5) 1975; 205 Gong (10.1016/S0252-9602(06)60066-0_bib1) 1998 Ahlfors (10.1016/S0252-9602(06)60066-0_bib11) 1966 Liu (10.1016/S0252-9602(06)60066-0_bib6) 1998; 19B |
| References_xml | – volume: 205 start-page: 389 year: 1975 ident: 10.1016/S0252-9602(06)60066-0_bib5 article-title: ϕ-like holomorphic functions in ℂn and Banach spaces publication-title: Trans Amer Math Soc – year: 1996 ident: 10.1016/S0252-9602(06)60066-0_bib13 – volume: 19B start-page: 401 issue: 4 year: 1998 ident: 10.1016/S0252-9602(06)60066-0_bib6 article-title: The growth theorem for star-like mappings on bounded star-like circular domains publication-title: Chin Ann of Math – year: 1998 ident: 10.1016/S0252-9602(06)60066-0_bib1 – year: 1962 ident: 10.1016/S0252-9602(06)60066-0_bib10 – volume: 22B start-page: 446 issue: 4 year: 2002 ident: 10.1016/S0252-9602(06)60066-0_bib14 article-title: The growth theorems for quasi-convex mappings on complex Hilbert spaces publication-title: Acta Math Sci doi: 10.1016/S0252-9602(17)30316-8 – year: 1966 ident: 10.1016/S0252-9602(06)60066-0_bib11 – volume: 210 start-page: 55 year: 1974 ident: 10.1016/S0252-9602(06)60066-0_bib8 article-title: Subordination chains and univalence of holomorphic mappings in ℂn publication-title: Math Ann doi: 10.1007/BF01344545 – year: 1999 ident: 10.1016/S0252-9602(06)60066-0_bib3 – year: 1960 ident: 10.1016/S0252-9602(06)60066-0_bib12 – volume: 39 start-page: 279 year: 1999 ident: 10.1016/S0252-9602(06)60066-0_bib9 article-title: Φ-like holomorphic mappings on balanced pseudoconvex domains publication-title: Complex Variables doi: 10.1080/17476939908815195 – volume: 142 start-page: 15 year: 1993 ident: 10.1016/S0252-9602(06)60066-0_bib2 article-title: Biholomorphic mappings in several complex variables publication-title: Contemporary Mathematics doi: 10.1090/conm/142/1208782 – year: 1963 ident: 10.1016/S0252-9602(06)60066-0_bib4 article-title: Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains publication-title: Amer Math Soc Transl Ser 6, Providence, RI – year: 1977 ident: 10.1016/S0252-9602(06)60066-0_bib7 article-title: Starlikness, convexity and other geometric properties of holomorphic mappings in higher dimensions doi: 10.1007/BFb0096834 |
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| Snippet | Let Ω be a bounded balanced pseudoconvex domain in C^n that admits a plurisubhamonic defining function of class C^2. The authors prove that if f is a... Let Omega be a bounded balanced pseudoconvex domain in n that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a... O4; Let Ω be a bounded balanced pseudoconvex domain in Cn that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a... |
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| Title | THE PARAMETRIC REPRESENTATION FOR SPIRAL-LIKE MAPPINGS OF TYPE α ON BOUNDED BALANCED PSEUDOCONVEX DOMAINS |
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