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Author |
Chuaqui, M.; Hernandez, R. |
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Title |
Families of homomorphic mappings in the polydisk |
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2023 |
Publication |
Complex Variables And Elliptic Equations |
Abbreviated Journal |
Complex Var. Elliptic. Equ. |
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Early Access |
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Keywords |
Schwarzian operator; polydiskl; ocally biholomorphic; norm; covering |
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We study classes of locally biholomorphic mappings defined in the polydisk P-n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes. |
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1747-6933 |
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WOS:001026714000001 |
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UAI @ alexi.delcanto @ |
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1841 |
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Author |
Efraimidis, I.; Gaona, J.; Hernandez, R.; Venegas, O. |
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Title |
On harmonic Bloch-type mappings |
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2017 |
Publication |
Complex Variables And Elliptic Equations |
Abbreviated Journal |
Complex Var. Elliptic Equ. |
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62 |
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8 |
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1081-1092 |
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Keywords |
Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30 |
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Let f be a complex-valued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent. |
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[Efraimidis, I.] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain, Email: iason.efraimidis@uam.es |
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Taylor & Francis Ltd |
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English |
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1747-6933 |
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WOS:000399938900004 |
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UAI @ eduardo.moreno @ |
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729 |
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