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Forelli-Rudin type theorem in pluriharmonic Bergman spaces with small index

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Science China Mathematics 1999年第12期42卷 1286-1291页

作者：任广斌史济怀 1. Department of Mathematics University of Science and Technology of China 230026 Hefei China

It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL p (B)∩h(B) onto Bergman spaceL p (B) ∩ H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that t... 详细信息

关键词： Bergman operator Gleason problem pluriharmonic functions.

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

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Acta Mathematica Scientia 2020年第1期40卷 35-44页

作者： Cao JIANG Xingtang DONG Zehua ZHOU School of Mathematics and Information Sciences Nanchang Hangkong UniversityNanchang 330063China School of Mathematics Tianjin UniversityTianjin 300350China

In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several ***,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the ***,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.

关键词： complex symmetric operator Toeplitz operator Bergman space pluriharmonic Bergman space

Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

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Acta Mathematica Sinica,English Series 2019年第10期35卷 1617-1628页

作者： Yin Yin HU Yu Feng LU Liu LIU Department of Mathematics Dalian Maritime UniversityDalian 116024P.R.China Department of Mathematics Dalian University of TechnologyDalian 116024P.R.China

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.

关键词： Toeplitz operator pluriharmonic symbols Dirichlet space

On the rigidity theorem for harmonic functions in Khler metric of Bergman type

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Science China Mathematics 2010年第3期53卷 779-790页

作者： LI Song-Ying 1,2, & WEI DongHuan 1 1 School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China 2 Department of Mathematics, University of California, Irvine, CA 92697-3875, USA 1. School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China2. Department of Mathematics University of California Irvine CA 92697-3875 USA

The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz 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).

关键词： rigidity pluriharmonic Laplace-Beltrami operators u-harmonic

Commuting Dual Toeplitz Operators on the Polydisk

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Chinese Quarterly Journal of Mathematics 2009年第1期24卷 63-68页

作者： CHENG Guo-zheng YU Tao Department of Mathematics Zhejiang Normal University Jinhua 321004 China

We completely characterize commutativity of S and Sψ on La2(Dn)⊥ for bounded pluriharmonic symbols  and ψ on Dn, and prove that SSψ = Sψ if and only if  is analytic or ψˉ is analytic.

关键词： Bergman space dual Toeplitz operator pluriharmonic