In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds axe obtained. By these, there exists a characterization of strongly isotropic pluriharmonic maps.
In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimens...In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P（Dn, BN） is C1＋α at z0 ∈ ErDn with f（0） = 0 and f（z0） = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =（λ1,0,…,λr,0,…,0）T∈R2 nsatisfying λi≥1/（22 n-1） for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.展开更多
1 Introduction Let Ω be a bounded symmetric domain in the complex vector space C<sup>n</sup>, 0∈Ω, with Bergman-Silov boundary b, Γ the group of holomorphic automorphisms of Ω and Γ<sub>0</s...1 Introduction Let Ω be a bounded symmetric domain in the complex vector space C<sup>n</sup>, 0∈Ω, with Bergman-Silov boundary b, Γ the group of holomorphic automorphisms of Ω and Γ<sub>0</sub> its isotropy group. It is known that Ω is circular and star-shaped with respect to 0 and that b is circular. The group Γ<sub>0</sub> is transitive on b and b has a unique normalized Γ<sub>0</sub>-invariant measure σ with σ（b）= 1. Hua constructed by group representation theory a system {φ<sub>k<sub>v</sub></sub>}展开更多
It is proved that the Bergman type operator T<sub>?</sub> is a bounded projection from the pluriharmonic Bergman space L<sup>p</sup>（B）∩h（B） onto Bergman space L<sup>p</sup>（...It is proved that the Bergman type operator T<sub>?</sub> is a bounded projection from the pluriharmonic Bergman space L<sup>p</sup>（B）∩h（B） onto Bergman space L<sup>p</sup>（B）∩H（B） for 0【p【1 and s】(p<sup>-1</sup>-1)（n+1）. As an application it is shown that the Gleason’s problem can be solved in Bergman space L<sup>P</sup>（B）∩H（B） for 0【p【1.展开更多
In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,man...In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,many non-trivial examples of(semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.展开更多
In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators t...In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same.Also,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.展开更多
The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these ...The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these metrics u ( u h = 0) in B n , then h must be pluriharmonic in B n . In fact, it is a characterization theorem, as a consequence, the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails. The results in this paper generalize the theorems of Graham (1983) and examples constructed by Graham and Lee (1988).展开更多
On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. B...On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.展开更多
基金Research supported by National Nature Science Foundation of China(10171012),Tian Yuan Foundation 10226001 and Foundation of Southeast University
文摘In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds axe obtained. By these, there exists a characterization of strongly isotropic pluriharmonic maps.
基金Supported by the Natural and Science Foundation of China(61379001,61771001)
文摘In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P（Dn, BN） is C1＋α at z0 ∈ ErDn with f（0） = 0 and f（z0） = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =（λ1,0,…,λr,0,…,0）T∈R2 nsatisfying λi≥1/（22 n-1） for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.
文摘1 Introduction Let Ω be a bounded symmetric domain in the complex vector space C<sup>n</sup>, 0∈Ω, with Bergman-Silov boundary b, Γ the group of holomorphic automorphisms of Ω and Γ<sub>0</sub> its isotropy group. It is known that Ω is circular and star-shaped with respect to 0 and that b is circular. The group Γ<sub>0</sub> is transitive on b and b has a unique normalized Γ<sub>0</sub>-invariant measure σ with σ（b）= 1. Hua constructed by group representation theory a system {φ<sub>k<sub>v</sub></sub>}
基金Project supported by the National Natural Science Foundation of China (Grant No. 19871081)the Doctoral Program Foundation of the State Education Commission of China
文摘It is proved that the Bergman type operator T<sub>?</sub> is a bounded projection from the pluriharmonic Bergman space L<sup>p</sup>（B）∩h（B） onto Bergman space L<sup>p</sup>（B）∩H（B） for 0【p【1 and s】(p<sup>-1</sup>-1)（n+1）. As an application it is shown that the Gleason’s problem can be solved in Bergman space L<sup>P</sup>（B）∩H（B） for 0【p【1.
基金supported by the National Natural Science Foundation of China(Nos.11201331,11771323).
文摘In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,many non-trivial examples of(semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.
基金supported in part by the National Natural Science Foundation of China(11201331,11771323)。
文摘In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same.Also,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.
文摘The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these metrics u ( u h = 0) in B n , then h must be pluriharmonic in B n . In fact, it is a characterization theorem, as a consequence, the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails. The results in this paper generalize the theorems of Graham (1983) and examples constructed by Graham and Lee (1988).
基金Supported by NSFC(Grant No.11871131)the Fundamental Research Funds for the Central Universities(Grant No.3132019177)
文摘On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.
