Related papers: Paired operators and paired kernels
In this paper we study the kernels of Toeplitz operators on both the scalar and the vector-valued Hardy space for $ 1 < p < \infty $. We show existence of a minimal kernel of any element of the vector-valued Hardy space and we determine a…
By the Hardy-Littlewood-Sobolev theorem the classical Riesz potential is bounded on Lebesgue spaces. E. Nakai and H. Sumitomo [16] extended that theorem to the Orlicz spaces. We introduce generalized potential operators on commutative…
The paper deals with the invertibility of Toeplitz plus Hankel operators T(a)+H(b) acting on classical Hardy spaces on the unit circle T. It is supposed that the generating functions a and b satisfy the condition a(t)a(1/t)=b(t)b(1/t).…
The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and $l^p$-spaces, integral and difference Wiener-Hopf plus Hankel operators and generalized Toeplitz plus Hankel operators. Special…
In this paper, existence of pairs of solutions is obtained for compact potential operators on Hilbert spaces. An application to a second-order boundary value problem is also given as an illustration of our results.
The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade. This manuscript investigates Liouville operators over the…
Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…
We formally introduce and study Toeplitz operators on the Hardy space of the $n$-dimensional Hartogs triangle. We find a precise relation between these operators and the Toeplitz operators on the Hardy space of the unit polydisc $\mathbb…
In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy…
The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in the complex plane. The norms for these…
In the recent paper by Mark C. Ho (2014) the notion of a $\lambda$-Toeplitz operator on the Hardy space $H^2(\mathbb{T})$ over the one-dimensional torus $\mathbb{T}$ was introduced and it was shown (under the supplementary condition) that…
We introduce a new class of conjugations and characterize complex symmetric Toeplitz operators on the Hardy space with respect to those conjugations. Also, we prove that complex symmetricity and \uet~ property are the same for a certain…
Asymmetric dual truncated Toeplitz operators acting between the orthogonal complements of two (eventually different) model spaces are introduced and studied. They are shown to be equivalent after extension to paired operators on…
We construct analogues of the Hecke operators for the moduli space of G-bundles on a curve X over a local field F with parabolic structures at finitely many points. We conjecture that they define commuting compact normal operators on the…
We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.
We consider bounded Hankel operators $H_{\psi}$ acting on the Hardy space $H^2$ to $L^2\ominus H^2$ and obtain results on the Schmidt subspaces $E^+_s(H_\psi)$ of such operators defined as the kernels of $ H_{\psi}^{\ast}H_{\psi}-s^2I$…
One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb{D}$ in the complex place $\mathbb{C}$ is to completely describe the commutant of a given Toeplitz operator, that is, the set of all…
In this paper, by using the atomic decomposition theory of Hardy space and weak Hardy space, we discuss the boundedness of parameterized Littlewood-Paley operator with variable kernel on these spaces.
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…
Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…