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.
We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for t...We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for the proof of the boundedness of composition operators,and then obtain an upper bound for the special operator norm on Bergman space.展开更多
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
In this paper, we discuss the Valiron＇s theorem in the unit polydisk D^N. We prove that for a holomorphic map φ：D^N→D^N satisfying some regular conditions, there exists a holomorphic map θ：D^N→H and a constant...In this paper, we discuss the Valiron＇s theorem in the unit polydisk D^N. We prove that for a holomorphic map φ：D^N→D^N satisfying some regular conditions, there exists a holomorphic map θ：D^N→H and a constant α〉 0 such that θ°φ=1/αθ. It is based on the extension of Julia-Wolff-Caratheodory （JWC） theorem of D in the polydisk.展开更多
We prove a reverse HSlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square ...We prove a reverse HSlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products TfTg are bounded invertible Toeplitz operators.展开更多
In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition ...In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain an upper bound for the operator norm on Lipschitz space.展开更多
In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
基金supported by the National Natural Science Foundation of China(11201199)the Scientific Research Foundation of Jinling Institute of Technology(Jit-b-201221)Qing Lan Project
文摘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.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(13ZB0101)
文摘We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for the proof of the boundedness of composition operators,and then obtain an upper bound for the special operator norm on Bergman space.
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.
基金Supported by the National Natural Science Foundation of China(11271359)
文摘In this paper, we discuss the Valiron＇s theorem in the unit polydisk D^N. We prove that for a holomorphic map φ：D^N→D^N satisfying some regular conditions, there exists a holomorphic map θ：D^N→H and a constant α〉 0 such that θ°φ=1/αθ. It is based on the extension of Julia-Wolff-Caratheodory （JWC） theorem of D in the polydisk.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971020)
文摘We prove a reverse HSlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk. Next, we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products TfTg are bounded invertible Toeplitz operators.
文摘In this paper, we define β-Hausdorff operator on the unit polydisk and study the boundedness of the operator on Lipschitz space. Firstly, we translate the problem of coefficient into integral of weighted composition operator, then give the sufficient conditions of boundedness, and also obtain an upper bound for the operator norm on Lipschitz space.
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
