Related papers: Boundedness of composition operators on Morrey spa…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
In this work, we study the composition operators on the little Lipschitz space ${\mathcal L}_0$ of a rooted tree $T$, defined as the subspace of the Lipschitz space ${\mathcal L}$ consisting of the complex-valued functions $f$ on $T$ such…
We show that a composition operator induced by an analytic self-map of the unit disc in the complex plane is weakly compact on the space BMOA precisely when the operator is compact on BMOA. As a crucial step we simplify the compactness…
We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted…
We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane $\mathbb{C}_+$ on the Hardy space $H^2(\mathbb{C}_+).$ We completely characterize which of these operators are cohyponormal and…
We show that the decay of approximation numbers of compact composition operators on the Dirichlet space $\mathcal{D}$ can be as slow as we wish, which was left open in the cited work. We also prove the optimality of a result of…
In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong…
In this paper, we provide some sufficient conditions for the compactness of weighted composition operators on Dirichlet space. Furthermore, we characterize the numerical range of certain classes of weighted composition operators on…
In this article, we completely characterize the Berezin range of Toeplitz operators with harmonic symbols acting on weighted Bergman spaces, illustrating the necessity of the harmonicity condition through examples. We then introduce a new…
We study singular perturbations of eigenvalues of the polyharmonic operator on bounded domains under removal of small interior compact sets. We consider both homogeneous Dirichlet and Navier conditions on the external boundary, while we…
Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_\omega$, where $0<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling…
In this article we extend recent results by the first author on the necessity of $BMO$ for the boundedness of commutators on the classical Lebesgue spaces. We generalize these results to a large class of Banach function spaces. We show that…
A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of…
It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Navanlinna counting function induces a reverse Carleson measure. Similar conclusion is not available on the Dirichlet space.…
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…
We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by…
It is known that the necessary and sufficient conditions of the boundedness of commutators on Morrey spaces are given by Di Fazio, Ragusa and Shirai. Moreover, according to the result of Cruz-Uribe and Fiorenza in 2003, it is given that the…
The aim of this paper is to get the boundedness of rough sublinear operators generated by fractional integral operators on vanishing generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the…
We consider generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\mathbb{R}^{n})$ including their weak versions $WM_{\Phi,\varphi}(\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(\varphi_{1},\varphi_{2})$ and $(\Phi, \Psi)$…
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…