An asymptotically sharp coefficients estimate for harmonic K-quasiconformal mappings

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• 作者：Hong-Ping Li
• 关键词：Heinz inequality ; Hübner inequalities ; coefficients estimate ; harmonic quasiconformal mapping
• 刊名：Journal of Inequalities and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,290 KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

By using the improved Hübner inequalities, in this paper we obtain an asymptotically sharp lower bound estimate for the coefficients of harmonic K-quasiconformal self-mappings of the unit disk \({\mathbb{D}}\) which keep the origin fixed. The result partly improves the former results given by (Partyka and Sakan in Ann. Acad. Sci. Fenn., Math. 30:167-182, 2005) and (Zhu and Zeng in J. Comput. Anal. Appl. 13:1081-1087, 2011). Furthermore, using some estimate for the derivative of the boundary function of a harmonic K-quasiconformal self-mapping w of \({\mathbb{D}}\) which keeps the origin fixed, we obtain an upper bound estimate for the coefficients of w.