A Study of the Higher-Order Schwarzian Derivatives of Hirotaka Tamanoi
-
Zhenyong Hu
,
Jinhua Fan
ABSTRACT
In this paper, we study the higher-order Schwarzian derivative Sn (f) proposed by H. Tamanoi [Higher Schwarzian operators and combinatorics of the Schwarzian derivative, Math. Ann. 305 (1996), 127–151]. For the strongly starlike functions of order α and strongly convex functions of order α, the sharp bound of |S 3(f)(0)| is obtained. When n ∈ [2, 7], we prove that the higher Bers maps induced by Sn (f) on Weil-Petersson Teichmüller space and BMO-Teichmüller space are holomorphic.
Acknowledgement
The authors would like to thank two anonymous reviewers for providing insightful comments and reading the manuscript carefully. This work is supported by the Fundamental Research Funds for the Central University (No. 30922010804), the Science and Technology Planning Project of Pingxiang City (No. 2020C0102) and the Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Technique Open Project (21zb03).
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© 2023 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- A Note on Special Subsets of the Rudin-Frolík Order for Regulars
- The 2-Class Group of Certain Families of Imaginary Triquadratic Fields
- The Deranged Bell Numbers
- On Index and Monogenity of Certain Number Fields Defined by Trinomials
- The k-Generalized Lucas Numbers Close to a Power of 2
- Shifted Power of a Polynomial with Integral Roots
- Further Insights into the Mysteries of the Values of Zeta Functions at Integers
- Memoryless Properties on Time Scales
- A Study of the Higher-Order Schwarzian Derivatives of Hirotaka Tamanoi
- Besov and Triebel-Lizorkin Capacity in Metric Spaces
- Oscillation of Odd Order Linear Differential Equations with Deviating Arguments with Dominating Delay Part
- An Elliptic Type Inclusion Problem on the Heisenberg Lie Group
- Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator
- A New Series Space Derived by Absolute Generalized Nörlund Means
- Examples of Weinstein Domains in the Complement of Smoothed Total Toric Divisors
- The Uniform Effros Property and Local Homogeneity
- Limit Theorems for Weighted Sums of Asymptotically Negatively Associated Random Variables Under Some General Conditions
- The Unit-Gompertz Quantile Regression Model for the Bounded Responses
- An Extended Gamma-Lindley Model and Inference for the Prediction of Covid-19 in Tunisia
- Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals
Articles in the same Issue
- A Note on Special Subsets of the Rudin-Frolík Order for Regulars
- The 2-Class Group of Certain Families of Imaginary Triquadratic Fields
- The Deranged Bell Numbers
- On Index and Monogenity of Certain Number Fields Defined by Trinomials
- The k-Generalized Lucas Numbers Close to a Power of 2
- Shifted Power of a Polynomial with Integral Roots
- Further Insights into the Mysteries of the Values of Zeta Functions at Integers
- Memoryless Properties on Time Scales
- A Study of the Higher-Order Schwarzian Derivatives of Hirotaka Tamanoi
- Besov and Triebel-Lizorkin Capacity in Metric Spaces
- Oscillation of Odd Order Linear Differential Equations with Deviating Arguments with Dominating Delay Part
- An Elliptic Type Inclusion Problem on the Heisenberg Lie Group
- Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator
- A New Series Space Derived by Absolute Generalized Nörlund Means
- Examples of Weinstein Domains in the Complement of Smoothed Total Toric Divisors
- The Uniform Effros Property and Local Homogeneity
- Limit Theorems for Weighted Sums of Asymptotically Negatively Associated Random Variables Under Some General Conditions
- The Unit-Gompertz Quantile Regression Model for the Bounded Responses
- An Extended Gamma-Lindley Model and Inference for the Prediction of Covid-19 in Tunisia
- Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals
