调和函数的高阶Schwarzian导数
Higher Order of Schwarzian Derivative of the Harmonic Functions
DOI: 10.12677/PM.2021.111007, PDF, HTML, 下载: 502  浏览: 680  国家科技经费支持
作者: 刘禹彤, 漆 毅：北京航空航天大学数学科学学院，北京
关键词: 调和函数；高阶Schwarzian导数；Harmonic Function； Higher Order of Schwarzian Derivative
摘要: 本文定义了调和函数的高阶Schwarzian导数形式，井证明了其仍具有Möbius不变性。其次，本文给出了调和函数的高阶Schwarzian导数的一种等价刻画。
Abstract: In this paper, we define the higher order of Schwarzian derivative of the harmonic functions. We also prove that it is still Möbius invariant. Finally, we give an equivalentcharacterization of the higher order of Schwarzian derivative of the harmonic functions.
文章引用：刘禹彤, 漆毅. 调和函数的高阶Schwarzian导数[J]. 理论数学, 2021, 11(1): 41-46. https://doi.org/10.12677/PM.2021.111007

参考文献

[1] Lewy, H. (1936) On the Non-Vanishing of the Jacobian in Certain One-to-One Mappings. Bulletin of the American Mathematical Society, 42, 689-692.
https://doi.org/10.1090/S0002-9904-1936-06397-4
[2] Hern´andez, R. and Mart´ın, M.J. (2015) Pre-Schwarzian and Schwarzian Derivatives of Har- monic Mappings. Journal of Geometric Analysis, 25, 64-91.
https://doi.org/10.1007/s12220-013-9413-x
[3] Hern´andez, R. and Mart´ın, M.J. (2017) On the harmonic M¨obius Transformations. eprint arXiv:1710.05952.
[4] Kim, S.-A. and Sugawa, T. (2011) Invariant Schwarzian Derivatives of Higher Order. Complex Analysis and Operator Theory, 5, 659-670.
https://doi.org/10.1007/s11785-010-0081-6
[5] Donaire, J.J. (2019) A Shimorin-Type Estimate for Higher-Order Schwarzian Derivatives. Computational Methods and Function Theory, 19, 315-322.
https://doi.org/10.1007/s40315-019-00265-0
[6] Tamanoi, H. (1996) Higher Schwarzian Operators and Combinatorics of the Schwarzian Deriva- tive. Mathematische Annalen, 305, 127-151.
https://doi.org/10.1007/BF01444214
[7] Cho, N.E., Kumar, V. and Ravichandran, V. (2018) Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes. Symmetry, 10, 348.
https://doi.org/10.3390/sym10080348
[8] 张兆功, 刘礼泉. 单叶调和映照的反函数[J]. 数学进展, 1996, 25(3): 270-276.

为你推荐