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

This paper considers composition operators on Zen spaces (a class of weighted Bergman spaces of the right half-plane related to weighted function spaces on the positive half-line by means of the Laplace transform). Generalizations are given…

The main themes of this survey are as follows: (a) the canonical (Riesz--Nevanlinna) factorization in various classes of analytic functions on the disk that are smooth up to its boundary, and (b) model subspaces (i.e., invariant subspaces…

We consider cyclic $m$-isometries on a complex separable Hilbert space. Such operators are characterized in terms of shifts on abstract spaces of weighted Dirichlet type. Our results resemble those of Agler and Stankus, but our model spaces…

For $0 \leq \alpha < n$ and $m \in \mathbb{N} \cap \left(1 - \frac{\alpha}{n}, +\infty \right)$, we consider certain fractional type operators $T_{\alpha, m}$ generated by $m$-orthogonal matrices and prove that, for $0 < \alpha < n$,…

We investigate some new classes of operator algebras which we call semi-$\sigma$-finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson's…

This paper studies the compressed shift operator $S_z$ on the Hardy space over the bidisk via the geometric approach. We calculate the spectrum and essential spectrum of $S_z$ on the Beurling type quotient modules induced by rational inner…

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

We prove that for operators satistying weighted inequalities with $A_p$ weights the boundedness on a certain class of Morrey spaces holds with weights of the form $|x|^\alpha w(x)$ for $w\in A_p$. In the case of power weights the shift with…

We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on…

This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_\theta^{\alpha}$ of order $\alpha$ and skewness…

The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…

In this paper we study $A$-projections, i.e. operators of a Hilbert space $\HH$ which act as projections when a seminorm is considered in $\HH$. $A$-projections were introduced by Mitra and Rao \cite{[MitRao74]} for finite dimensional…

We show that if a nonscalar operator on a separable Hilbert space has a nontrivial invariant subspace, then it has also a nontrivial hyperinvariant subspace. Thus the hyperinvariant subspace problem is equivalent to the invariant subspace…

Let $(\mathcal{X},d,\mu)$ be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ satisfying the Davies--Gaffney estimate, and $X(\mathcal{X})$ a ball…

A general class of weighted multilinear Hardy-Ces\`aro operators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on…

We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $\Lambda^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the…

We define a scale of weighted Morrey spaces which contains different weighted versions appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the…

Let $0 \leq \alpha < n$, $N \in \mathbb{N}$, and let $X$ and $Y$ be ball quasi-Banach function spaces on $\mathbb{R}^n$. We consider operators $T_{\alpha}$ defined by convolution with kernels of type $(\alpha, N)$. Assuming that the powered…

In this paper, the authors prove the boundedness of commutators generated by the weighted Hardy operator on weighted $\lambda$-central Morrey space with the weight $\omega$ satisfying the doubling condition. Moreover, the authors give the…