Let G be a bounded open set on the complex plane, we denote by La2(G) the totality of all analytic functions on G which is square intergrable with respect to Lebesgue measure dA on G. It’s clear that La2(G) is a Hilb...Let G be a bounded open set on the complex plane, we denote by La2(G) the totality of all analytic functions on G which is square intergrable with respect to Lebesgue measure dA on G. It’s clear that La2(G) is a Hilbert space when endowed with norm ‖f‖=(∫G|f|2dA)1/2. The bounded operator S on La2(G) which is multiplication by z will be callde Bergman operator on G. For Bergman operators we have the following properties ([1], [4]):展开更多
This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition o...This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.展开更多
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...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 this paper.展开更多
In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not h...In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .展开更多
THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ ...THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).展开更多
Forα〉1,let dvαdenote the weighted Lebesgue measure on the bidisk andμa complex measure satisfying some Carleson-type conditions.In this paper,we show a sufcient and necessary condition for the Toeplitz operatorT...Forα〉1,let dvαdenote the weighted Lebesgue measure on the bidisk andμa complex measure satisfying some Carleson-type conditions.In this paper,we show a sufcient and necessary condition for the Toeplitz operatorTαˉμto be bounded or compact on weighted Bergman spaceL1a（dvα）.展开更多
Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of...Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.展开更多
文摘Let G be a bounded open set on the complex plane, we denote by La2(G) the totality of all analytic functions on G which is square intergrable with respect to Lebesgue measure dA on G. It’s clear that La2(G) is a Hilbert space when endowed with norm ‖f‖=(∫G|f|2dA)1/2. The bounded operator S on La2(G) which is multiplication by z will be callde Bergman operator on G. For Bergman operators we have the following properties ([1], [4]):
基金Supported by the NNSF of China(10471039)the Natural Science Foundation of Zhejiang Province(M103 104)the Natural Science Foundation of Huzhou City(2005YZ02).
文摘This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11671065)
文摘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 this paper.
基金supported by National Natural Science Foundation of China(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.2013jjB 0050)Simons Foundation(Grant No.196300)
文摘In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .
文摘THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).
基金Supported by National Nature Science Foundation of China(Grant Nos.10971195 and 11271332)Natural Science Foundation of Zhejiang Province(Grant No.LQ12A01004)
文摘Forα〉1,let dvαdenote the weighted Lebesgue measure on the bidisk andμa complex measure satisfying some Carleson-type conditions.In this paper,we show a sufcient and necessary condition for the Toeplitz operatorTαˉμto be bounded or compact on weighted Bergman spaceL1a（dvα）.
基金supported by the National Natural Science Foundation of China(Nos.11101139,11271124)the Natural Science Foundation of Zhejiang Province(Nos.Y6090036,Y6100219)the Foundation of Creative Group in Universities of Zhejiang Province(No.T200924)
文摘Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.
