Hua Domains Research Articles

On the Product of Weighted Composition Operators and Radial Derivative Operators from the Bloch-Type Space into the Bers-Type Space on the Fourth Loo-Keng Hua Domain

Let HEIV be the fourth Loo-Keng Hua domain. We study the boundedness of the product of the weighted composition operator and the radial derivative operator from the Bloch-type space Bα(HEIV) into the Bers-type space Aβ(HEIV) and provide the necessary and sufficient conditions for their boundedness.

Composition Operators on Weighted Zygmund Spaces of the First Loo-keng Hua Domain

Let HEI denote the first Loo-keng Hua domain. In this paper, we obtain many elementary results on HEI by the continuous and careful discussions. In some applications, we obtain some necessary conditions or sufficient conditions for the boundedness and compactness of the composition operators on weighted Zygmund space defined on HEI.

Boundedness and Compactness of Weighted Composition Operators from α-Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind

We address weighted composition operators ψCϕ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators.

On the Rigidity of Proper Holomorphic Self-Mappings of the Hua Domains

On the Rigidity of Proper Holomorphic Self-Mappings of the Hua Domains

The Holomorphic Equivalence of Two Equidimensional Hartogs Domains over Bounded Symmetric Domains

This paper is concerned with the biholomorphism of two equidimensional Hartogs type domains over irreducible bounded symmetric domains $H_{\Omega}(p)$ (see (1.1)) which is a Hua construction of Cartan–Hartogs domain. We develop a new simple methods to give an sufficient and necessary condition for the two Hua domains to be biholomorphic equivalent by using the function $\mathcal{L}_{\Omega}(z,\omega)$ (see (1.2)). Furthermore as an application, we can also give an equivalent description for the automorphism of Hua domain.

Metrics and rigidity on Hartogs-type domains

This paper mainly deals with the metrics and rigidity on some Hartogs-type domains in several complex variables. Firstly, we describe the Bergman kernel expansions of canonical metrics for the Hartogs domains over bounded symmetric domains, and we also obtain necessary and sufficient conditions for the canonical metrics to be balanced metrics. Secondly, we give the rigidity of proper holomorphic mappings on several Hartogs domains (i.e., Hua domains, Foc k -Bargmann-Hartogs domains and pentablock).

Boundedness and compactness of the composition operators from <italic>u</italic>-Bloch space to <italic>v</italic>-Bloch space on the first Hua domains

In this paper, we introduce a weighted Bloch space and discuss the boundedness and compactness of composition operators Cφ from the u -Bloch space βu (HE I ) to the v -Bloch space βv (HE I ), and obtain the necessary condition and sufficient condition on the boundedness and compactness of composition operators Cφ on the first Hua domains.

Rigidity of proper holomorphic mappings between equidimensional Hua domains

Hua domain, named after Chinese mathematician Loo-Keng Hua, is defined as a domain in $${\mathbb {C}}^{n}$$ fibered over an irreducible bounded symmetric domain $$\Omega \subset {\mathbb {C}}^{d}$$ with the fiber over $$z\in \Omega $$ being a $$(n-d)$$ -dimensional generalized complex ellipsoid $$\Sigma (z)$$ . In general, a Hua domain is a nonhomogeneous bounded pseudoconvex domain without smooth boundary. The purpose of this paper is twofold. Firstly, we obtain what seems to be the first rigidity results on proper holomorphic mappings between two equidimensional Hua domains. Secondly, we determine the explicit form of the biholomorphisms between two equidimensional Hua domains. As a special conclusion of this paper, we completely describe the group of holomorphic automorphisms of the Hua domain.

On automorphism groups of generalized Hua domains

AbstractHua domains, generalized Hua domains and Hua constructions, named after the great Chinese mathematician Luogeng Hua (Loo-Keng Hua), are generalizations of Cartan–Hartogs domains introduced by Weiping Yin around the end of the 20th century. In this paper, we give a complete description of automorphism groups of generalized Hua domains. We also discuss the corresponding problem for Hua constructions.

Lu Qi-Keng conjectue and Hua domain

The first part of this paper discusses the motivation for the Lu Qi-Keng conjecture and the results about the presence or the absence of zeroes of the Bergman kernel function of a bounded domain in ℂn. Its second part summarizes the main results on the Hua domains, such as the explicit Bergman kernel function, the comparison theorem for the invariant metrics, the explicit complete Einstein-Kahler metrics, the equivalence between the Einstein-Kahler metric and the Bergman metric, etc.

The equivalence on classical metrics

In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, and prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau's Schwarz lemma we prove that the new metrics are equivalent to the Einstein-Kahler metric. That means that the Yau's conjecture is true on Cartan-Hartogs domains.

Extremal problems on the generalized Hua domain of the first type*

Abstract Abstract Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained. *Supported by National Natural Science Foundation of China (Grant No. 10471097)

Extremal problems on the Hua domain of the first type

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

THE EINSTEIN KÄHLER METRIC WITH EXPLICIT FORMULAS ON SOME NON-HOMOGENEOUS DOMAINS

In this paper we describe the Einstein-Kahler metric for the Cartan-Hartogs domains which are the special case of the Hua domains. First of all, we reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(z,w). This differential equation can be solved to give an implicit function in X. Secondly, for some cases, we obtained explicit forms of the complete Einstein-Kahler metrics on Cartan-Hartogs domains which are the non-homogeneous domains.

THE EINSTEIN-KÄHLER METRICS ON HUA DOMAIN

In this paper we describe the Einstein-Kahler metric for the Cartan-Hartogs of the first type which is the special case of the Hua domains. Firstly, we reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, w) = <TEX>$\midw\mid^2[det(I-ZZ^{T}]^{\frac{1}{K}}$</TEX> (see below). This differential equation can be solved to give an implicit function in Χ. Secondly, we get the estimate of the holomorphic section curvature under the complete Einstein-K<TEX>$\ddot{a}$</TEX>hler metric on this domain.

Bergman kernel on generalized exceptional hua domain

We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function

The Bergman kernel functions on Hua domains

We get the Bergman kernel functions in explicit formulas on four types of Hua domain. There are two key steps: First, we give the holomorphic automorphism groups of four types of Hua domain; second, we introduce the concept of semi-Reinhardt domain and give their complete orthonormal systems. Based on these two aspects we obtain the Bergman kernel function in explicit formulas on Hua domains.