Related papers: A note on composition operators on the bidisc

The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel\'{a}ez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for…

The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…

Let $\phi(z)=(\phi_1(z), ...,\phi_n(z))$ be a holomorphic self-map of $U^n$ and $\psi(z)$ a holomorphic function on $U^n,$ where $U^n$ is the unit polydisk of ${\Bbb C}^n.$ Let $p\geq 0,$ $q\geq 0$, this paper gives some necessary and…

In this paper we investigate composition operators on discrete spaces. We establish the classification of underlying graphs of such operators. For one class of such graphs, namely graphs with one cycle, we obtain a characterization of…

We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…

Let $\phi$ be a quasiconformal mapping, and let $T_\phi$ be the composition operator which maps $f$ to $f\circ\phi$. Since $\phi$ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins…

In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{D})$ invariant under the composition operator $C_{\phi_a}f=f\circ\phi_a$, where $\phi_a(z) = az + 1 - a$ for $a \in (0,1)$ is an…

It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two…

In the present paper we study perturbation theory for the $L^p$ Dirichlet problem on bounded chord arc domains for elliptic operators in divergence form with potentially unbounded antisymmetric part in BMO. Specifically, given elliptic…

We investigate the structure of norm-preserving and linear but not necessarily surjective operators on variable-exponent, discrete Lebesgue spaces. A certain class of isometries, novel to this work, are especially considered; this class…

Every function in the Dirichlet space on the unit disc has an inner/outer factorization. We study which inner functions occur in this way. For Blaschke products, this is the well known question of which subsets of the disc are zero sets for…

Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_\omega$ to the Lebesgue space $L^q_\nu$, where $0<q<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights…

A high-frequency asymptotics of the symbol of the Dirichlet-to-Neumann map, treated as a periodic pseudodifferential operator, in 2D diffraction problems is discussed. Numerical results support a conjecture on a universal limit shape of the…

In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a…

Bounded and unbounded weighted composition operators on $L^2$ spaces over $\sigma$-finite measure spaces are investigated. A variety of questions related to seminormality of such operators are discussed.

The aim of this paper is to give the answer to the problem of characterization of acting conditions (necessary as well as sufficient) for composition operators in some sequence spaces. We also characterize their boundedness and local…

In this note, we aim to describe sharp constants for the composition operator with a bi-Lipschitz measure-preserving map in several functional spaces (BMO, Hardy space, Carleson measures, ...). It is interesting to see how the measure…

In this paper, the authors first discuss the characterization of Herz Triebel-Lizorkin spaces with variable exponent via two families of operators. By this characterization, the authors prove that the Lipschitz commutators of sublinear…

In this paper we consider composition operators on Harmonic-Bloch type spaces and we compute the spectrum of composition operators. Also, we characterize isometric composition operators on harmonic Bloch type spaces.

Let $\phi$ be an analytic self-map and $u$ be a fixed analytic function on the open unit disk $D$ in the complex plane $\CC.$ The weighted composition operator is defined\break by \begin{equation*} uC_\phi f =u \cdot (f\circ \phi), f \in…