Shaolin Chen, Antti Rasila
In this paper, we will give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk. Our main results are generalizations of results of Colonna for planar harmonic mappings in [Indiana Univ. Math. J. 38: 829--840, 1989].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Coefficient bounds and growth estimates for a class of pluriharmonic mappings in unit polydisk
研究单位多圆盘上一类由二阶偏导数和特定界定义的归一化多重调和映射$\mathcal{P}_{\mathcal{H}_n^0}(M)$，通过证明与全纯函数类的对应关系，给出其函数的精确系数界和增长估计。
On a class of pluriharmonic mappings in the unit polydisk
研究单位多圆盘上归一化多重调和映射的\(\mathcal{W}_{\mathcal{H}_n^0}(\alpha)\)类，通过建立与全纯函数类的对应扩展相关结果，还得到该类函数的系数界、增长估计等，且引入并研究了其截面的性质。
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions from the Euclidean unit ball in $\mathbb{R}^n$ into the unit ball of the real Minkowski space. Next, we give several sharp Schwarz-Pick type inequalities for pluriharmonic functions from the Euclidean unit ball in $\mathbb{C}^n$ or from the unit polydisc in $\mathbb{C}^n$ into the unit ball of the Minkowski space. Furthermore, we establish some sharp coefficien…
Multidimensional analogues of the improved Bohr's inequality for shifted polydisks
研究\(\mathbb{C}^n\)中一般单连通域上全纯函数的玻尔现象，改进相关现有结果，还考虑含单位多圆盘的多圆盘上多重调和映射，建立玻尔型不等式。
A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in ${\mathbb C}^n$ are introduced. Basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic. Furthermore, it is shown that if the Schwarzian derivative of a pluriharmonic mapping vanishes then the analytic part of this mapping is a Möbius transformation. Some o…
The Schwarz lemma as one of the most influential results in complex analysis and it has a great impact to the development of several research fields, such as geometric function theory, hyperbolic geometry, complex dynamical systems, and theory of quasi-conformal mappings. In this note we mainly consider various version of Schwarz lemma and its relatives related to holomorphic functions including several variables.
The main purpose of this paper is to develop some methods to investigate the Schwarz type lemmas of holomorphic mappings and pluriharmonic mappings in Hilbert and Banach spaces. Initially, we extend the classical Schwarz lemmas of holomorphic mappings to Hilbert and Banach spaces. Furthermore, we improve and generalize the classical Schwarz lemmas of planar harmonic mappings into the sharp forms of Banach spaces, and present some applications to sharp boundary Schwarz type lemmas for pluriharmonic mappings in Hilbert and Banach spaces and the obtained results provide the improvements and gener…
There is a known generalization of the classical Schwarz lemma to holomorphic functions from the polydisk to the disk. In this paper, we characterize those functions which satisfy equality everywhere in this generalized inequality: they are the transfer function of an n+1 by n+1 symmetric unitary, and in particular, are rational, inner, and belong to the Schur-Agler class of the polydisk. We also present some sufficient conditions for a function to be of this type.
The main purpose of this paper is to develop some methods to investigate the Schwarz type lemmas of holomorphic mappings and pluriharmonic mappings in Banach spaces. Initially, we extend the classical Schwarz lemmas of holomorphic mappings to Banach spaces, and then we apply these extensions to establish a sharp Bloch type theorem for pluriharmonic mappings on homogeneous unit balls of $\C^n$ and to obtain some sharp boundary Schwarz type lemmas for holomorphic mappings in Banach spaces. Furthermore, we improve and generalize the classical Schwarz lemmas of planar harmonic mappings into the sh…
On Stable Univalence and Coefficient Estimates for a Class of Pluriharmonic Mappings in Convex Reinhardt Domains
本文研究了凸Reinhardt域中双曲映射的稳定性与系数估计，通过多维Noshiro-Warschawski定理的推广，建立了双曲映射与全纯函数的一一对应关系，并给出了尖锐的系数估计。
In this paper, we first establish a Schwarz-Pick type theorem for pluriharmonic mappings and then we apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, we obtain several Landau's and Bloch's type theorems for pluriharmonic mappings.
The notion of a unitary realization is used to estimate derivatives of arbitrary order of functions in the Schur-Agler class on the polydisk and unit ball.
Families of Homomorphic Mappings in the Polydisk
本文研究多圆盘中 Bergman 度量下 Schwarzian 算子有界的局部双全纯映射族，建立相关微分方程解的性质，并利用修改类的 Lipschitz 连续性估计原始类的阶。
The Schwarzian Derivative for Convex Holomorphic Mappings in Several Complex Variables
本文研究了几复变量中凸全纯映射的Schwarz导数范数上界，推导出在多变量情况下的精确估计，扩展了经典一维结果，并给出了Roper-Suffridge扩展算子的最佳界。
On the Boundary Schwarz lemma and the rigidity theorem for certain mappings
本文研究了从$B_{\ell_p^n} imes\mathbb{D}^{m}$到$\mathbb{D}^{m}$的全纯映射，给出了向量值全纯函数的边界Schwarz引理的简明证明，并扩展了现有结果，同时获得了单位球$B_{\ell_p^n}$上多调和自映射的边界Schwarz引理，以及对于$B_{\ell_p^n}$的全纯自映射的边界刚性定理。
Schwarz-Pick type inequalities from an operator theoretical point of view
从算子理论视角，利用von Neumann不等式证明并推广了Schwarz-Pick型不等式，包括多点情形、算子版本及多圆盘与高阶导数情形，并借助判别簇增强了双圆盘上的Schwarz-Pick引理。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。