Related papers: Toeplitz and Ces\`aro-Type Operators on Homogeneou…
In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson…
Let $F^{2,m}(\mathbb{C})$ denote the Fock-Sobolev space of complex plane. In this paper, we characterize the semi-commutator of two Toeplitz operators on $F^{2,m}(\mathbb{C})$ is zero. The result is different from the result of Bauer, Choe,…
We study Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting on wavelet subspaces…
We consider a class of compact Toeplitz operators on the Bergman space on the unit disk. The symbols of operators in our class are assumed to have a sufficiently regular power-like behaviour near the boundary of the disk. We compute the…
This paper is about the operators defined between K\"othe spaces whose associated matrix is a Hankel matrix. After demonstrating how these operators are defined, the conditions for continuity and compactness of these operators are…
We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive line bundle. We associate to a function with compact support…
We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with $\cC^k$--\,symbol on a symplectic manifold. We also give a semi-classical estimate of the distance of a Toeplitz operator to the space of…
On the weakly pseudo-convex domains $\Omega_p^n$ we introduce quasi-homogeneous quasi-radial symbols. These are used to prove the existence of a commutative Banach algebra of Toeplitz operators on Bergman space of $\Omega_p^n$. We also show…
Given a regular weight $\omega$ and a positive Borel measure $\mu$ on the unit disc $\mathbb{D}$, the Toeplitz operator associated with $\mu$ is $$ \mathcal{T}_\mu(f)(z)=\int_{\mathbb{D}} f(\zeta)\bar{B_z^\omega(\zeta)}\,d\mu(\zeta), $$…
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…
In this paper, we characterize the Hartogs domains over homogeneous Siegel domains of type II and explicitly describe their automorphism groups. Moreover we prove that any proper holomorphic map between Hartogs domains over homogeneous…
In this paper, we consider Hankel operators, with locally integrable symbols, densely defined on a family of Fock-type spaces whose weights are $C^3$-logarithmic growth functions with mild smoothness conditions. It is shown that a Hankel…
Motivated by the work of Nazarov and Shapiro on the unit disk, we study asymptotic Toeplitzness of composition operators on the Hardy space of the unit sphere in C^n. We extend some of their results but we also show that new phenomena…
We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of $p$-Fock spaces $(1\leq p \leq \infty)$. We present an overview of recent results by various authors…
We study the ranks of commutators and generalized semicommutators of Toeplitz operators with quasihomogeneous symbols on both the harmonic Bergman space and the Bergman Space. In particular, when one of quasihomogeneous symbols is the the…
We aim to contribute to the folklore of function spaces on Lipschitz domains. We prove the boundedness of the trace operator for homogeneous Sobolev and Besov spaces on a special Lipschitz domain with sharp regularity. To achieve this, we…
For $1 < p < \infty$ let $\mathcal{T}_p ^\alpha$ be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space $F_\alpha ^p$. In this paper, we will show that an operator…
Toeplitz plus Hankel operators $T(a)+H(b)$, $a,b\in L^\infty$ acting on the classical Hardy spaces $H^p, 1<p<\infty$, are studied. If the generating functions $a$ and $b$ satisfy the so-called matching condition $a(t) a(1/t)=b(t) b(1/t)$,…
In this paper, we study necessary and sufficient conditions for a positive Borel measure $\mu$ on the complex space $\mathbb{C}$ to be a $(\infty,q)$ or $(p,\infty)$ (vanishing) Fock-Carleson measure through its Berezin transform. Then we…
Let $T_{f}$ denote the Toeplitz operator on the Hardy space $H^{2}(\mathbb{T})$ and let $T_{n}(f)$ be the corresponding $n \times n$ Toeplitz matrix. In this paper, we characterize the compactness of the operators…