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In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…
In this paper we continue the study of free holomorphic functions on the unit ball of B(H)^n, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Several classical results from complex analysis have free…
In this paper, the main aim is to demonstrate the boundedness for commutators of (fractional) maximal function and sharp maximal function in the slice spaces, where the symbols of the commutators belong to the BMO space, whereby some new…
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…
When G is a region in the complex plane, compact composition operators on the uniform algebra of bounded analytic functions on G and the spectra of these operators were described by D. Swanton, Compact composition operators on B(D), Proc.…
We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…
The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…
The Korenblum space, often referred to as a growth space, is a special type of analytic function space. This paper investigates the properties of the difference of composition operators on the Korenblum space over the product of upper half…
We study the compactness of composition operators on the Bergman spaces of certain bounded convex domains in $\mathbb{C}^n$ with non-trivial analytic discs contained in the boundary. As a consequence we characterize that compactness of the…
In this paper, we introduce new spaces of holomorphic functions on the unit ball $\mathbb{B}_{n}$ of $\mathbb{C}^{n}$ generalizing the classical Bergman spaces. The main results include the properties of some operators and integrals…
In this work, the density in $H(b)$ spaces of finitely connected planar domains and the boundedness of composition operators on these function spaces are studied. Density of the algebra $\mathcal{A}(D)$ is considered for both in the cases…
The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman--type" singular integral operators. The canonical example of such an operator is the…
We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev and Besov norms in $L_{p}$-spaces on compact Riemannian manifolds. The proofs rely on estimates for the near-diagonal localization of the…
The survey is devoted to diverse applications of Besov classes in operator theory. It is illustrated how Besov classes are used to describe Hankel operators of Schatten--von Neumann classes; various applications of this description are…
We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…
We consider a dilation operator on Besov spaces $(B^s_{r,t}(K))$ over local fields and estimate an operator norm on such a field for $s > \sigma_r = \text{max}\big(\frac{1}{r} -1,~0\big)$ which depends on the constant $k$ unlike the case of…
We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we…
In this paper, we study the boundedness and essential norms of the differences of two generalized composition operators acting from $\alpha$-Bloch space to $\beta$-Bloch space on the open unit disk. From essential norms, we get the…