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Algebraic Properties of Toeplitz and Small Hankel Operators on the harmonic bergman space

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Acta Mathematica Sinica,English Series 2014年第8期30卷 1395-1406页

作者： Hong Yan GUAN Yu Feng LU School of Mathematical Sciences Dalian University of Technology School of Mathematics and Systems Science Shenyang Normal University

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.

关键词： Toeplitz operator small Hankel operator quasihomogeneous symbols harmonic bergman space Mellin transform

Dual Toeplitz Operators on the Orthogonal Complement of the harmonic bergman space

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Acta Mathematica Sinica,English Series 2021年第7期37卷 1143-1155页

作者： Yang PENG Xian Feng ZHAO Cancer Center Daping HospitalArmy Medical University(Third Military Medical University)Chongqing 400038P.R.China College of Mathematics and Statistics Chongqing UniversityChongqing 401331P.R.China

In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic bergman space.This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the bergman space due to Stroethoff and Zheng’s paper[Trans.Amer.Math.Soc.,354,2495–2520(2002)].

关键词： Dual Toeplitz operator harmonic bergman space

Positivity of Toeplitz Operators on harmonic bergman space

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Acta Mathematica Sinica,English Series 2016年第2期32卷 175-186页

作者： Yong Lu SHU Xian Feng ZHAO College of Mathematics and Statistics Chongqing University Shanghai Center for Mathematical Sciences Fudan University

In this paper, we study positive Toeplitz operators on the harmonic bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.

关键词： Positive Toeplitz operators harmonic bergman space Berezin transform

Zero Products and Finite Rank of Toeplitz Operators on the harmonic bergman space

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Journal of Mathematical Research with Applications 2017年第3期37卷 325-334页

作者： Qian DING Yinyin HU Liu LIU Yufeng LU School of Mathematical Sciences Dalian University of Technology Department of Mathematics Dalian Maritime University

We study zero product problem and finite rank of the Brown-Halmos type results involving products of Toeplitz operators acting on the harmonic bergman space. We use the Berezin transform and invariant Laplacian in thi... 详细信息

关键词： Toeplitz operator finite rank harmonic bergman space

Algebraic Properties of Toeplitz Operators on the harmonic bergman space

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Journal of Mathematical Research with Applications 2016年第4期36卷 495-504页

作者： Jingyu YANG Yufeng LU Xiaoying WANG School of Mathematics and Statistics Chifeng University Department of Mathematics Dalian University of Technology

In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic bergman space. Next, we characterize finite rank commutators and semi-com... 详细信息

关键词： Toeplitz operator harmonic bergman space quasihomogeneous commutator finite rank