Related papers: Extremal Non-Compactness of Composition Operators …

In this work we study the essential spectra of composition operators on weighted Bergman spaces of analytic functions which might be termed as "quasi-parabolic." This is the class of composition operators on $A_{\alpha}^{2}$ with symbols…

In this paper, we give some estimates for the norm and essential norm of the differences of two composition operators between different Hardy spaces.

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…

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…

We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…

In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of Hardy-Littlewood maximal studied by Antezana…

A Hilbert space operator $U$ is called universal (in the sense of Rota) if every Hilbert space operator is similar to a multiple of $U$ restricted to one of its invariant subspaces. It follows that the Invariant Subspace Problem for Hilbert…

In this paper, we study 2-complex symmetric composition operators with the conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the necessary and sufficient condition for the composition operator $C_\phi$ to be 2-complex…

Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$, and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators…

Let $\phi$ be an analytic map taking the unit disk $\mathbb{D}$ into itself. We establish that the class of composition operators $f \mapsto C_\phi(f) = f \circ \phi$ exhibits a rather strong rigidity of non-compact behaviour on the Hardy…

We completely characterize the mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$. In particular, we show that a composition operator acting on this space is mean ergodic if and only if it is uniformly mean ergodic.

We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…

In this paper we use orthonormal basis for the Hardy space $H^{2}(\mathbb{T})$, formed by rational functions, to characterize complex symmetric Toeplitz operators on $H^{2}(\mathbb{T})$. As a result, we get examples of these operators whose…

Let H^2(D) denote the classical Hardy space of the open unit disk D in the complex plane. We obtain descriptions of both the spectrum and essential spectrum of composition operators on H^2(D) whose symbols belong to the class S(2)…

We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators…

We study the $H$-convergence of nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. Our compactness argument bypasses the failure of the classical…

We investigate Hardy spaces $H^1_L(X)$ corresponding to self-adjoint operators $L$. Our main aim is to obtain a description of $H^1_L(X)$ in terms of atomic decompositions similar to such characterisation of the classical Hardy spaces…

Let $\mathscr{H}^2$ denote the Hardy space of Dirichlet series $f(s) = \sum_{n\geq1} a_n n^{-s}$ with square summable coefficients and suppose that $\varphi$ is a symbol generating a composition operator on $\mathscr{H}^2$ by…

We study weighted composition operators on quasi-Banach spaces of holomorphic functions via their induced action on jets along periodic orbits. Under a natural graded nondegeneracy condition, boundedness and compactness, together with a…