Related papers: Essential norm of composition operators Harmonic B…
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 generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^\Psi$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^\Psi$;…
A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…
The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete…
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators…
Given a symbol $\varphi,$ i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator $C_{\varphi}(f)=f\circ\varphi$ defined on the Banach spaces of holomorphic functions $A(\mathbb{D})$ and…
In this work we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here we begin the study of the iterations of the functions of…
In this paper, we investigate Li-Yorke composition operators and some of their variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in…
We study the boundedness of composition operators on the weighted Bergman spaces and the Hardy space over the polydisc. For arbitrary polydisc we prove the rank sufficiency theorem which, in particular, provides us with a simple criterion…
We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from…
In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type…
First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on $L^1+L^\infty$ with…
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…
We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…
In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…
The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calder\'on-Zygmund operators in harmonic…
We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…
We study composition operators whose symbols are suitable perturbations of the identity and which act between different weighted modulation classes. We consider both modulation spaces formed by tempered distributions and those whose…
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…