Related papers: Positivity, complex FIOs, and Toeplitz operators
Invertibility of Toeplitz operators on the Bergman space and the related Douglas problem are long standing open problems. In this paper we study the invertibility problem under the novel geometric condition on the image of the symbols,…
We look at Toeplitz operators $T_\nu$ on the Fock Space (also known as the Segal-Bargmann space) which have a positive Borel measure $\nu$ as a symbol. We characterize when $\left(T_\nu\right)^s$ for $0<s\leq 1$ is in the symmetrically…
In this paper, we discuss hyponormal block Toeplitz operators $T_{\Phi}$ over the vector-valued weighted Bergman space $A_\alpha^2\left(\mathbb{C}^n\right)$. And two conditions about hyponormal block Toeplitz operators $T_{\Phi}$ on…
We characterize boundedness and compactness of pullback operators under holomorphic maps between Bargmann spaces of entire holomorphic functions with quadratic strictly plurisubharmonic exponential weights, extending a result of…
The paper contains a survey of a class of Fourier integral operators defined by symbols with tempered weight. These operators are bounded (respectively compact) in $L^2$ if the weight of the amplitude is bounded (respectively tends to $0$).
Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we…
We study the boundedness of Toeplitz operators $T_\psi$ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of $\mathbb{R}^n$. Generalizing earlier results for analytic function spaces, we derive a general…
We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for…
In this article, we completely characterize the Berezin range of Toeplitz operators with harmonic symbols acting on weighted Bergman spaces, illustrating the necessity of the harmonicity condition through examples. We then introduce a new…
For any given bounded symmetric domain, we prove the existence of commutative $C^*$-algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of the Toeplitz operators that generate such algebras are defined…
In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We completely characterized every case of the bounded and compact Toeplitz operators on the weighted Bergman…
In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear…
We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…
We characterize bounded Toeplitz and Hankel operators from weighted Bergman spaces to weighted Besov spaces in tube domains over symmetric cones. We deduce weak factorization results for some Bergman spaces of this setting.
We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…
We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function $\omega$ and suitable window function $\fy $, the Toeplitz operator (or localization operator) $\tp_\fy…
We investigate Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic operator on cones, both under Navier and Dirichlet boundary conditions. Moreover, we study existence and qualitative properties of extremal functions. In…
Let $m \geq 1$ be an integer and let $H_m(\mathbb B)$ be the analytic functional Hilbert space on the unit ball $\mathbb B \subset \mathbb C^n$ given by the reproducing kernel $K_m(z,w) = (1 - \langle z,w \rangle)^{-m}$. We prove that…
The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…
Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators. Whereas the boundedness properties of frame multipliers on…