Related papers: Boundedness and compactness of weighted compositio…

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

We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal…

We compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the Hardy and weighted Bergman spaces of the upper half-plane. We are also able to extend the results to weighted Dirichlet spaces…

Doubling metric measure spaces provide a natural framework for singular integral operators. In contrast, the study of maximally modulated singular integral operators, the so-called Carleson operators, has largely been limited to Euclidean…

We study compact operators on the Bergman space of the Thullen domain defined by $\{(z_1,z_2)\in \mathbb C^2: |z_1|^{2p}+|z_2|^2<1\}$ with $p>0$ and $p\neq 1$. The domain need not be smooth nor have a transitive automorphism group. We give…

Let \(0<q<p<\infty\), \(\Omega\) be a bounded \(\bbC\)-convex domains in \(\bbC^n\). We establish several equivalent characterizations for the boundedness of Carleson embedding \(J_\mu:A_\alpha^p\hookrightarrow L^q(\mu)\) on \(\Omega\) with…

In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear…

In this paper we solve a long standing problem about the bilinear $T1$ theorem to characterize the (weighted) compactness of bilinear Calder\'{o}n-Zygmund operators. Let $T$ be a bilinear operator associated with a standard bilinear…

We give a necessary and sufficient condition for a holomorphic self-map $\phi$ of the tridisc to induce a bounded composition operator on the associated Hardy space. This condition depends on the behaviour of the first and the second…

We reduce the boundedness of operators in Morrey spaces $L_p^r({\mathbb R}^n)$, its preduals, $H^{\varrho}L_p ({\mathbb R}^n)$, and their preduals $\overset{\circ}{L}{}^r_p({\mathbb R}^n)$ to the boundedness of the appropriate operators in…

We prove weak $(2,2)$ bounds for maximally modulated anisotropically homogeneous smooth multipliers on $\mathbb{R}^n$. These can be understood as generalizing the classical one-dimensional Carleson operator. For the proof we extend the…

In this paper we investigate weighted composition operators between weak and strong vector valued weighted Bergman spaces and Hardy spaces.

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…

We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson…

The aim of this paper is to get the boundedness of certain sublinear operators with rough kernel generated by Calder\'on-Zygmund operators on the generalized weighted Morrey spaces under generic size conditions which are satisfied by most…

The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were…

We consider this and related questions: When is a finite linear combination of composition operators, acting on the Hardy space or the standard weighted Bergman spaces on the unit disk, a compact operator?

This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are…

We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…