Related papers: An introduction to composition operators in Sobole…
We show that Brennan's conjecture is equivalent to boundedness of composition operators on homogeneous Sobolev spaces generated by conformal homeomorphisms of simply connected plane domains to the unit disc.
We characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces
In this paper we deal with unbounded composition operators defined in Orlicz spaces. Indeed, we provide some necessary and sufficient condition for densely definedness of composition operators on Orlicz spaces. Also, we will investigate the…
In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…
We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…
Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
We study extension operators on Sobolev spaces with decreasing integrability on the base of set functions associated with the operator norms. Sharp necessary conditions in the terms of the generalized density condition and the terms of weak…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
This note characterizes both boundedness and compactness of a composition operator between any two analytic Campanato spaces on the unit complex disk.
The continouity and compactness of embedding operators in in Sobolev-Lions type spaces are derived. By applying this result separability properties of degenerate anisotropic differential operator equations, well-posedeness and Strichartz…
This paper is based on three hours of lectures given by the first author in the "Focus Program on Analytic Function Spaces and their Applications" July 1 -- December 31, 2021, organized by the Fields Institute for Research in Mathematical…
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 characterize essential norm of composition operators on the spaces of Harmonic Bloch functions. These results extends the similar results that were proven for composition operators on Bloch spaces.
We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We characterize these spaces as real interpolation of natural order intrinic…
We study invertibility of bounded composition operators of Sobolev spaces. The problem is closely connected with the theory of mappings of finite distortion. If a homeomorphism $\varphi$ of Euclidean domains $D$ and $D'$ generates by the…
The purpose of this paper is to describe the characterization for the compact difference of two composition operators acting between analytic Besov spaces and the weighted little Bloch type space over the unit disk.
The study of what we now call Sobolev inequalities has been studied for almost a century in various forms, while it has been eighty years since Sobolev's seminal mathematical contributions. Yet there are still things we don't understand…