Related papers: Weighted Hardy spaces: shift invariant and coinvar…

In this paper, we study operator-theoretic properties of the compressed shift operators $S_{z_1}$ and $S_{z_2}$ on complements of submodules of the Hardy space over the bidisk $H^2(\mathbb{D}^2)$. Specifically, we study Beurling-type…

Let $\nu = (\nu_1, \ldots, \nu_n) \in (-1/2, \infty)^n$, with $n \ge 1$, and let $\Delta_\nu$ be the multivariate Bessel operator defined by \[ \Delta_{\nu} = -\sum_{j=1}^n\left( \frac{\partial^2}{\partial x_j^2} - \frac{\nu_j^2 -…

Let $\mathbb H$ be the finite direct sums of $H^2(\mathbb D)$. In this paper, we give a characterization of the closed subspaces of $\mathbb H$ which are invariant under the shift, thus obtaining a concrete Beurling-type theorem for the…

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of…

We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of…

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 classical Hardy space theory of square-summable Taylor series in the complex unit disk there is a circle of ideas connecting Szeg\"o's theorem, factorization of positive semi-definite Toeplitz operators, non-extreme points of the…

The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant…

We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of $C_0^\infty(\mathbb{R}^n)$ in Morrey norm. We show that these subspaces are…

In this paper, we consider several questions emerging from the Beurling-Lax-Halmos Theorem, which characterizes the shift-invariant subspaces of vector-valued Hardy spaces. The Beurling-Lax-Halmos Theorem states that a backward…

In this paper we study canonical models for representations of the Hardy algebras that generalize the model theory of Sz.-Nagy and Foias for contraction operators. The Hardy algebras are non selfadjoint operator algebras associated with…

We study factorizations of operator valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions from weighted Schur classes and so-called ``conservative curved'' systems introduced…

This paper explores various classes of invariant subspaces of the classical Ces\`{a}ro operator $C$ on the Hardy space $H^2$. We provide a new characterization of the finite co-dimensional $C$-invariant subspaces, based on earlier work of…

In this paper, we establish the two weight commutator of Calder\'on--Zygmund operators in the sense of Coifman--Weiss on spaces of homogeneous type, by studying the weighted Hardy and BMO space for $A_2$ weight and by proving the sparse…

A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ \|T_1\xi_1+T_2\xi_2+... +T_d\xi_d\|^2\leq \|\xi_1\|^2+\|\xi_2\|^2+...+\|\xi_d\|^2 $ for all…

Let $\mathcal L=-\Delta+V$ be a Schr\"odinger operator, where $\Delta$ is the Laplacian on $\mathbb R^d$ and the nonnegative potential $V$ belongs to the reverse H\"older class $RH_q$ for $q\geq d$. The Riesz transform associated with the…

Let ${\mathcal X}$ be a metric space with doubling measure, $L$ a nonnegative self-adjoint operator in $L^2({\mathcal X})$ satisfying the Davies-Gaffney estimate, $\omega$ a concave function on $(0,\infty)$ of strictly lower type…

For the Hardy-Littlewood maximal and Calder\'on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak…

Let $(\mathbb{X},d,\mu)$ be a space of homogeneous type in the sense of R. R. Coifman and G. Weiss, and $X(\mathbb{X})$ a ball quasi-Banach function space on $\mathbb{X}$. In this article, the authors introduce the weak Hardy space…

This dissertation summarizes my investigations in operator theory during my PhD studies. The first chapter is an introduction to that field of operator theory which was developed by B. Sz.-Nagy and C. Foias, the theory of power-bounded…