Related papers: Nuclear Weighted composition operators between dif…

In the paper, we consider integral operators with non-negative kernels satisfying conditions, which are less restrictive than conditions studied earlier. We establish criteria for the boundedness of these operators in Lebesgue spaces.

In the context of analytic functions on the open unit disk, a weighted composition operator is simply a composition operator followed by a multiplication operator. The class of weighted composition operators has an important place in the…

Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical…

We study topologizability and power boundedness of weigh\-ted composition operators on (certain subspaces of) $\mathscr{D}'(X)$ for an open subset $X$ of $\mathbb{R}^d$. For the former property we derive a characterization in terms of the…

We determine exactly when two classes of integral operators are bounded on weighted $L^p$ spaces over the Siegel upper half-space.

While there have been extensive studies regarding the theory of composition operators in standard Bergman spaces, there have not been many results pertaining to large Bergman spaces due to a lack of useful tools. In this paper, we give the…

We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|x\|_p=1\} \,\geq \,p^{-\frac{1}{p}}…

Inspired by Schwartz, Jang-Lewis and Victory, who study in particular generalizations of triangularizations of matrices to operators, we shall give for positive operators on Lebesgue spaces equivalent definitions of atoms (maximal…

In this note we prove that if a sublinear operator T satisfies a certain weighted estimate in the $L^{p}(w)$ space for all $w\in A_{p}$, $1<p<+\infty$, then the operator norm of T on $L^{p}(w)$ is a continuous function of the weight $w$,…

We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition…

We study monomial operators on $ L^2[0,1]$, that is bounded linear operators that map each monomial $x^n$ to a multiple of $x^{p_n}$ for some $p_n$. We show that they are all unitarily equivalent to weighted composition operators on a Hardy…

We study some important topological properties such as boundedness, compactness and essential norm of differences of weighted composition operators between Fock spaces

In this paper we completely describe the numerical range of Toeplitz operators on weighted Bergman spaces with harmonic symbol. We also characterize the numerical range of weighted composition operators on weighted Bergman spaces and…

In this note, we consider a class of composition operators on Lebesgue spaces with variable exponents over metric measure spaces. Taking advantage of the compatibility between the metric-measurable structure and the regularity properties of…

Let $\msp$ be a purely non-atomic measure space, and let $1 < p < \infty$. If $\weakLp\msp$ is isomorphic, as a Banach space, to $\weakLp\mspp$ for some purely atomic measure space $\mspp$, then there is a measurable partition $\Omega =…

In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations),…

We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.

In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…

This note characterizes both boundedness and compactness of a composition operator between any two analytic Campanato spaces on the unit complex disk.

Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…