Schwarz-Pick Estimates Research Articles

On Harnack inequality and harmonic Schwarz lemma

AbstractIn this paper, we study the $(s, C(s))$ -Harnack inequality in a domain $G\subset \mathbb {R}^n$ for $s\in (0,1)$ and $C(s)\geq 1$ and present a series of inequalities related to $(s, C(s))$ -Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under K-quasiconformal and K-quasiregular mappings, where $K\geq 1$ . Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz–Pick estimate for a real-valued harmonic function.

A refinement of the Schwarz-Pick estimates and the Carathéodory metric in several complex variables

A refinement of the Schwarz-Pick estimates and the Carathéodory metric in several complex variables

The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables

The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables

A Refinement of Schwarz–Pick Lemma for Higher Derivatives

In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita.

Higher-order Schwarz-Pick estimates for holomorphic self-mappings on classical domains

In this paper, Schwarz-Pick estimates for high order Frechet derivatives of holomorphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Schwarz-Pick estimates of higher-order partial derivatives for bounded holomorphic functions on classical domains.

The Generalized Schwarz–Pick Estimates of Arbitrary Order on the Unit Polydisk

Let Ω be a homogeneous circular convex domain (a bounded symmetric domain) in \({\mathbb{C}^N}\) containing the origin. The generalization of the Schwarz–Pick estimates of partial derivatives of arbitrary order are established for holomorphic mappings from the unit polydisk D n to Ω associated with the Caratheodory metric. The metric enables us to obtain some known results from a unified perspective and also leads some new results. In particular, our results are valid for the Cartan domains. When Ω = B N , the Schwarz–Pick estimates of high order reduces to that of Liu and Chen.

Schwarz-pick estimates for bounded holomorphic functions on classical domains

In this paper, Schwarz-Pick estimates for high order Fréchet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.

Schwarz-Pick estimates for partial derivatives of arbitary order of bounded holomorphic functions in the unit ball of ℂ n

This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of ℂ n .

Schwarz–Pick estimates for holomorphic mappings from the polydisk to the unit ball

In this paper, Schwarz–Pick estimates of arbitrary order partial derivatives for holomorphic mappings from the polydisk to the unit ball are presented. We generalize the early work on Schwarz–Pick estimates of higher order derivatives for bounded holomorphic functions on the unit disk and the polydisk.

The high order Schwarz-Pick lemma on complex Hilbert balls

In this paper we prove a high order Schwarz-Pick lemma for holomorphic mappings between unit balls in complex Hilbert spaces. In addition, a Schwarz-Pick estimate for high order Frechet derivatives of a holomorphic function f of a Hilbert ball into the right half-plane is obtained.

Schwarz-Pick estimates for bounded holomorphic functions in the unit ball of ℂ n

We give a Schwarz-Pick estimate for bounded holomorphic functions on unit ball in ℂn, and generalize some early work of Schwarz-Pick estimates for bounded holomorphic functions on unit disk in ℂ.

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and Dn, and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on unit disk in ℂ.

A note on Schwarz-Pick estimate

A Schwarz-Pick estimate of higher order derivative for holomorphic functions with positive real part on Bn is presented. This improves the earlier work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on the unit disk in ℂ.

Note on Schwarz-Pick estimates for bounded and positive real part analytic functions

Note on Schwarz-Pick estimates for bounded and positive real part analytic functions

Hyperbolic derivatives and generalized Schwarz-Pick estimates

In this paper we use the beautiful formula of Faa di Brune for the nth derivative of composition of two functions to obtain the generalized Scliwarz-Pick estimates. By means of those estimates we show that the hyperbolic derivative of an analytic self-map of the unit disk is Lipschitz with respect to the pseudohyperbolic metric.