Related papers: Sobolev algebra through a "carr\'e du champ" ident…
The present paper is devoted to a theory of profile decomposition for bounded sequences in \emph{homogeneous} Sobolev spaces, and it enables us to analyze the lack of compactness of bounded sequences. For every bounded sequence in…
In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…
The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type…
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…
We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the…
A CP semigroup is a semigroup of normal unit-preserving completely positive maps acting on the algebra B(H) of all operators on a separable Hilbert space H. Such a semigroup has a natural generator L; since the individual maps of the…
In this paper, we focus on the functional and geometrical aspects of the fractional Sobolev capacity, the Besov capacity and the Riesz capacity on stratified lie groups, respectively. Firstly, we provide a new Carleson characterization of…
We use a model operator approach and the spectral theorem for self-adjoint operators in a Hilbert space to derive the basic results of abstract left-definite theory in a straightforward manner. The theory is amply illustrated with a variety…
In this paper, we give a sharp sparse domination of pseudodifferential operators associated with symbols belonging to the H\"{o}rmander class, and fundamental solutions of dispersive equations. Furthermore, we give boundedness results of…
In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism $\varphi: \Omega \to\widetilde{\Omega}$ belongs to the Sobolev space $L^{1}_{q}(\Omega;…
In a doubling metric measure space $(X,\rho,\mu)$ supporting a Poincar\'e inequality, we give a new characterisation of first-order Sobolev spaces by mean oscillations, and extend previous characterisations of constant functions in terms of…
We study an increasing family of spaces ${\mathcal{B}_{k}^{p}}_{1\leq p\leq \infty}$ by adapting the techniques used in the study of Beurling algebras by Coifman and Meyer (1978). A weak form Wiener-Levy theorem is proved based on an…
In this paper we connect Calder\'on and Zygmund's notion of $L^p$\- -differentiability with some recent characterizations of Sobolev spaces via the asymptotics of non-local functionals due to Bourgain, Brezis, and Mironescu. We show how the…
We extend in this article the classical Sobolev inequalities for the module of continuity for the functions belonging to the integer order Sobolev's space on the Sobolev-Bilateral Grand Lebesgue spaces. As a consequence, we deduce the…
For a continuous function $f:\mathbb{R}\to\mathbb{R}$, define the corresponding graph by setting \[\Gamma_f := {(x1, f(x1)) : x_1\in\mathbb{R}} .\] In this paper, we study the Sobolev extension property for the upper and lower domains over…
In this article we study a class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions. We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we…
In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and $Q$-mappings. On this base we obtain measure distortion properties $Q$-homeomorphisms. Using the composition operators on…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since our approach comes from harmonic analysis, we establish…
We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…