Hartogs域上延拓算子的性质
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摘要
主要研究Roper-Suffridge延拓算子在推广的Hartogs域上的性质.借助双全纯映照的偏差定理,得到延拓算子在Ω_N上保持强α次殆β型螺形映照、α次殆β型螺形映照和α次β型螺形映照的性质,进而得到B~n上相应的结论.所得结论包含已有的结果并为研究C~n中的双全纯映照提供了新的途径.
This paper mainly discuss the properties of the generalized Roper-Suffridge operators on the extended Hartogs domains. By using the distortion results of subclasses of biholomorphic mappings, the authors conclude that the generalized operators preserve the properties of strong and almost spirallike mappings of type β and order α,almost spirallike mappings of type β and order a, spirallike mappings of type β and order a on Ω_N under different conditions, respectively. Thus the authors get the corresponding results on B~n.These conclusions involve some known results and provide new approaches to research the biholomorphic mappings in C~n.
This paper mainly discuss the properties of the generalized Roper-Suffridge operators on the extended Hartogs domains. By using the distortion results of subclasses of biholomorphic mappings, the authors conclude that the generalized operators preserve the properties of strong and almost spirallike mappings of type β and order α,almost spirallike mappings of type β and order a, spirallike mappings of type β and order a on Ω_N under different conditions, respectively. Thus the authors get the corresponding results on B~n.These conclusions involve some known results and provide new approaches to research the biholomorphic mappings in C~n.
引文
[1] Roper K A, Suffridge T J. Convex mappings on the unit ball of C~n[J]. J Anal Math,1995, 65:333-347.
[2] Graham I, Kohr G. Univalent mappings associated with the Roper-Suffridge extension operator[J]. J Analyse Math, 2000, 81:331-342.
[3]刘小松,刘太顺.关于α次的β型螺形映照推广的Roper-Suffridge算子[J].数学年刊A辑,2006, 27(6):789-798.
[4]刘小松,冯淑霞.关于α次的β型螺形映射推广的Roper-Suffridge算子的一个注记[J].数学季刊,2009, 24(2):310-316.
[5]刘浩,夏红川.Reinhardt域上一类推广的Roper-Suffridge算子[J].数学学报,2016,59(2):253-266.
[6] Muir J R. A modification of the Roper-Suffridge extension operator[J]. Comput Methods Funct Theory, 2005, 5(1):237-251.
[7] Kohr G. Loewner chains and a modification of the Roper-Suffridge extension operator[J]. Mathematica, 2006, 71(1):41-48.
[8]王建飞,刘太顺.全纯映射子族上改进的Roper-Suffridge算子[J].数学年刊A辑,2010,31(4):487-496.
[9] Muir J R. A class of Loewner chain preserving extension operators[J]. J Math Anal Appl, 2008, 337(2):862-879.
[10]唐言言.Bergman-Hartogs型域上的Roper-Suffridge算子[D].开封:河南大学硕士论文,2016.
[11]潘利双,王安.Bergman-Hartogs型域的全纯自同构群[J].中国科学,2015, 45:31-42.
[12]叶薇薇,王安.一类Hartogs域的Einstein-K(a|¨)hler度量和Kobayashi度量的比较定理[J].数学年刊A辑,2012, 33(6):687-704.
[13] Wang A, Liu Y. Zeroes of the Bergman kernels on some new Hartogs domains[J]. Chin Quart J of Math, 2011, 26(3):325-334.
[14]蔡荣华,刘小松.强螺形函数子族的第三项和第四项系数估计[J].湛江师范学院学报,2010, 31:38-43.
[15] Zhu Y C, Liu M S. The generalized Roper-Suffridge extension operator on Reinhardt domain D_p[J]. Taiwanese Jour of Math, 2010, 14(2):359-372.
[16] Feng S, Liu T. The generalized Roper-Suffridge extension operator[J]. Acta Math Sci,2008, 28B(1):63-80.
[17]冯淑霞,刘太顺,任广斌.复Banach空间单位球上几类映射的增长掩盖定理[J].数学年刊A辑,2007, 28(2):215-230.
[18] Liu T S, Ren G B. The growth theorem for starlike mappings on bounded starlike circular domains[J]. Chin Ann Math, Ser B, 1998, 19(4):401-408.
[19] Ahlfors L V. Complex analysis[M]. 3rd, ed. New York:Mc Graw-Hill Book Co., 1979.
[20] Duren P L. Univalent functions[M]. New York:Springer-Verlag, 1983.
[21] Graham I, Kohr G. Geometric function theory in one and higher dimensions[M]. New York:Marcel Dekker, 2003.
[22]张洁,卢金.单位多圆柱上α次的殆β型螺形映射的偏差定理[J].湖州师范学院学报,2011, 33(2):46-50.
[23]王朝君,崔艳艳,刘浩.B~n上推广的Roper-Suffridge算子的性质[J].数学学报,2016,59(6):721-864.
[2] Graham I, Kohr G. Univalent mappings associated with the Roper-Suffridge extension operator[J]. J Analyse Math, 2000, 81:331-342.
[3]刘小松,刘太顺.关于α次的β型螺形映照推广的Roper-Suffridge算子[J].数学年刊A辑,2006, 27(6):789-798.
[4]刘小松,冯淑霞.关于α次的β型螺形映射推广的Roper-Suffridge算子的一个注记[J].数学季刊,2009, 24(2):310-316.
[5]刘浩,夏红川.Reinhardt域上一类推广的Roper-Suffridge算子[J].数学学报,2016,59(2):253-266.
[6] Muir J R. A modification of the Roper-Suffridge extension operator[J]. Comput Methods Funct Theory, 2005, 5(1):237-251.
[7] Kohr G. Loewner chains and a modification of the Roper-Suffridge extension operator[J]. Mathematica, 2006, 71(1):41-48.
[8]王建飞,刘太顺.全纯映射子族上改进的Roper-Suffridge算子[J].数学年刊A辑,2010,31(4):487-496.
[9] Muir J R. A class of Loewner chain preserving extension operators[J]. J Math Anal Appl, 2008, 337(2):862-879.
[10]唐言言.Bergman-Hartogs型域上的Roper-Suffridge算子[D].开封:河南大学硕士论文,2016.
[11]潘利双,王安.Bergman-Hartogs型域的全纯自同构群[J].中国科学,2015, 45:31-42.
[12]叶薇薇,王安.一类Hartogs域的Einstein-K(a|¨)hler度量和Kobayashi度量的比较定理[J].数学年刊A辑,2012, 33(6):687-704.
[13] Wang A, Liu Y. Zeroes of the Bergman kernels on some new Hartogs domains[J]. Chin Quart J of Math, 2011, 26(3):325-334.
[14]蔡荣华,刘小松.强螺形函数子族的第三项和第四项系数估计[J].湛江师范学院学报,2010, 31:38-43.
[15] Zhu Y C, Liu M S. The generalized Roper-Suffridge extension operator on Reinhardt domain D_p[J]. Taiwanese Jour of Math, 2010, 14(2):359-372.
[16] Feng S, Liu T. The generalized Roper-Suffridge extension operator[J]. Acta Math Sci,2008, 28B(1):63-80.
[17]冯淑霞,刘太顺,任广斌.复Banach空间单位球上几类映射的增长掩盖定理[J].数学年刊A辑,2007, 28(2):215-230.
[18] Liu T S, Ren G B. The growth theorem for starlike mappings on bounded starlike circular domains[J]. Chin Ann Math, Ser B, 1998, 19(4):401-408.
[19] Ahlfors L V. Complex analysis[M]. 3rd, ed. New York:Mc Graw-Hill Book Co., 1979.
[20] Duren P L. Univalent functions[M]. New York:Springer-Verlag, 1983.
[21] Graham I, Kohr G. Geometric function theory in one and higher dimensions[M]. New York:Marcel Dekker, 2003.
[22]张洁,卢金.单位多圆柱上α次的殆β型螺形映射的偏差定理[J].湖州师范学院学报,2011, 33(2):46-50.
[23]王朝君,崔艳艳,刘浩.B~n上推广的Roper-Suffridge算子的性质[J].数学学报,2016,59(6):721-864.