Article
Mathematics, Applied
Nina Zorboska
Summary: We prove the strong localization of a Toeplitz operator with a complex Borel measure symbol whose total variation is Carleson, thus improving recent localization results by Sadeghi and Zorboska [J. Math. Anal. Appl. 485 (2020), p. 16]. We also show that this result provides another perspective on previously known results concerning Toeplitz operators with BMO symbols.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Shubham R. Bais, D. Venku Naidu
Summary: In this article, we discuss the structure of L-invariant operators on F2(Cn) where L is a Lagrangian plane. We focus on Toeplitz operators Ta with L-invariant symbols a E Lm(Cn) and show that they can be represented as integral operators. Furthermore, we prove that an operator H?X is in the C*-algebra TL(Lm) if and only if there exists m E Cb,u(Rn) satisfying certain conditions on the function ?.
COMPLEX ANALYSIS AND OPERATOR THEORY
(2023)
Article
Mathematics, Applied
Siyu Wang, Zipeng Wang
Summary: In this paper, boundedness and compactness of Toeplitz operators T-mu,T-beta between distinct weighted Bergman spaces L-a(p)(omega(alpha)) and L-a(q)(omega(beta)) are discussed. The results obtained in this study are new and extend previous findings in unweighted Bergman spaces.
SCIENCE CHINA-MATHEMATICS
(2022)
Article
Mathematics
Wolfram Bauer, Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner
Summary: We establish a new criterion for ensuring the self-adjointness of Toeplitz operators with unbounded operator-valued symbols. Specifically, our criterion is applicable to symbols with Lipschitz continuous derivatives, which are commonly used in classical mechanics as Hamiltonian functions. To achieve this, we extend the Berger-Coburn estimate to vector-valued Segal-Bargmann spaces. Additionally, we demonstrate the application of our result in proving the self-adjointness of a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schrodinger representation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Ermin Wang, Jiajia Xu
Summary: This paper investigates the boundedness and compactness of Toeplitz operators between two large Fock spaces, which has significant implications in the fields of computer science and mathematics.
Article
Mathematics, Applied
Hong Rae Cho, Hyungwoon Koo, Young Joo Lee
Summary: In this study, we focus on the orthogonal complement of the polyanalytic Fock space to investigate the properties of dual Toeplitz operators. We characterize the zero sum of products of two dual Toeplitz operators with harmonic symbols. Our results extend several known results on the analytic Fock space to every polyanalytic Fock spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics
Guangfu Cao, Li He, Yiyuan Zhang
Summary: In this paper, reverse Carleson measures for a class of generalized Fock spaces F-phi(p) with 0 < p < infinity and with phi satisfying dd(c) phi similar or equal to omega(0) are characterized. Several equivalent characterizations for invertible Toeplitz operators T psi, induced by positive bounded symbols psi on F-phi(2), are obtained as applications of these results.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Mathematics
Zhengyuan Zhuo, Zengjian Lou
Summary: We provide a complete characterization of the sampling measures mu for a family of Fock space F-phi(p) (0 < p < infinity) induced by a non-radial doubling weight through the refinement of (mu) over cap (r) and related dominating sets. Using this characterization, we demonstrate that the conditions (mu) over cap, 1/(mu) over capr being an element of L-infinity or (mu) over tilde, 1/(mu) over tilde being an element of L-infinity do not guarantee the measurability of mu as a sampling measure on Fock spaces.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
Yongjiang Duan, Kunyu Guo, Siyu Wang, Zipeng Wang
Summary: In this paper, by using Carleson measures and T1-type conditions, necessary and sufficient conditions for a positive Borel measure μ are obtained, and the problems related to the Toeplitz operator are studied. Furthermore, a generalization of a previous research result is presented.
JOURNAL OF GEOMETRIC ANALYSIS
(2022)
Article
Mathematics
Chunxu Xu, Tao Yu
Summary: We characterize the necessary and sufficient conditions for invertible Toeplitz operators acting on the Fock space. Specifically, we study the Fredholm properties of Toeplitz operators with BMO1 symbols, where their Berezin transforms are bounded functions of vanishing oscillation. By examining the winding of the Berezin transform along a sufficiently large circle, we show the Fredholm index of the Toeplitz operator and provide a characterization for invertible Toeplitz operators with non-negative symbols that may be unbounded, but have bounded and oscillation-vanishing Berezin transforms.
Article
Mathematics, Applied
Changbao Pang, Antti Perala, Maofa Wang, Xin Guo
Summary: In this paper, the boundedness of the maximal operator on the upper half-plane π+ is proven. Here, π+ is equipped with a positive Borel measure dω(y)dx satisfying the doubling property ω((0, 2t))≤Cω((0, t)). This result is connected to the Carleson embedding theorem, which is used to characterize the boundedness and compactness of the Volterra type integral operators on the Bergman spaces Apω(π+).
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Jianhui Hu, Songxiao Li, Dan Qu
Summary: This paper provides complete characterizations of positive Borel measures that lead to bounded or compact differentiation operators in Fock spaces. It also discusses the boundedness and compactness of generalized weighted composition operators in Fock spaces, as well as studies the essential norm of these operators.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Hicham Arroussi, Hua He, Junfeng Li, Cezhong Tong
Summary: In this paper, we provide a complete characterization of bounded and compact Toeplitz operators between different large Fock spaces F-omega(p) and F-omega(q) with 0 < p, q <= infinity. We use average functions, certain generalized Berezin transforms, and Carleson measures to achieve this characterization. We also characterize the essential norms of Toeplitz operators from F-omega(p) into F-omega(q) for 0 < p, q <= infinity.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Nihat Gokhan Gogus, Sinem Yelda Sonmez
Summary: We focus on the study of weighted Bergman spaces on finitely connected planar domains and find that they are isomorphic to the product of weighted Bergman spaces on the unit disk. By utilizing this, we successfully characterize Carleson embeddings and prove kernel estimates. We also characterize bounded, compact and Schatten class composition and Toeplitz operators on these spaces. Our results generalize several recent findings in the unit disk or simply connected case.
ANNALS OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Jun Tao Du, Song Xiao Li, Hasi Wulan
Summary: In this paper, a universal description of the boundedness and compactness of Toeplitz operator T-mu(omega) between Bergman spaces is provided, taking into consideration certain conditions such as the measure mu being a positive Borel measure, 1 < p, q < infinity, and regular weights omega, eta, upsilon. By utilizing Khinchin's inequality and Kahane's inequality, a new characterization of the Carleson measure for Bergman spaces induced by regular weights is obtained.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2023)
