相关论文: Indefinite Schwarz-Pick inequalities on the bidisk…
In this short note, we will give a generalization of the indefinite Schwarz-Pick inequality due to Seto [8]. Our approach is based on a connection between complex geometry and the geometry of reproducing kernel Hilbert spaces, which was…
We prove a kind of "reverse Schwarz--Pick lemma" for holomorphic self-maps of the disk. The result becomes especially clear-cut for inner functions and casts new light on their derivatives.
We use (versions of) the von Neumann inequality for Hilbert space contractions to prove several Schwarz-Pick inequalities. Specifically, we derive an alternate proof for a multi-point Schwarz-Pick inequality by Beardon and Minda, along with…
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.
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings between the unit balls in complex spaces. This extends the classical Schwarz-Pick lemma and the related result proved by Pavlovic.
In this paper we establish several invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for holomorphic selfmaps of strongly convex domains in $\mathbb C^N$ in the spirit of…
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…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
The purpose of this paper is to study the Schwarz-Pick type inequality and the Lipschitz continuity for the solutions to the nonhomogeneous biharmonic equation: $\Delta(\Delta f)=g$, where $g:$ $\overline{\ID}\rightarrow\mathbb{C}$ is a…
Based on the recently proved Khavinson conjecture, we establish an inequality of Schwarz-Pick type for harmonic functions on the unit ball of $\mathbb{R}^n$.
We extend the classical Schwarz-Pick inequality to the class of harmonic mappings between the unit disk and a Jordan domain with given perimeter. It is intriguing that the extremals in this case are certain harmonic diffeomorphisms between…
We prove some sharp inequalities for complex harmonic functions on the unit disk. The results extend a M. Riesz conjugate function theorem and some well-known estimates for holomorphic functions. We apply some of results to the…
In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of $\alpha$-harmonic equation for $\alpha>-1$ are investigated. By making use of the integral of trigonometric functions, we obtain the two types of…
We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self-maps of the unit disk. In particular, we discuss the case of infinitely many critical points and its relation to the…
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…
This paper establishes a sharp Schwarz-Pick type inequality for real-valued invariant harmonic functions defined on the complex unit ball $\mathbb B^n$. The proof of this main result simultaneously provides a solution to a natural extension…
We derive some integral inequalities for holomorphic maps between complex manifolds. As applications, some rigidity and degeneracy theorems for holomorphic maps without assuming any pointwise curvature signs for both the domain and target…
In this note we establish a Schwarz type inequality for holomorphic mappings between unit balls $B_n$ and $B_m$ in corresponding complex spaces.
We consider the multi-point Schwarz-Pick lemma and its associate functions due to Beardon-Minda and Baribeau-Rivard-Wegert. Basic properties of the associate functions are summarized. Then we observe that special cases of the multi-point…
We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective…