Related papers: Trace and extension operators for fractional Sobol…

While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid…

In this work, firstly in the direct sum of Hilbert spaces of vector-functions L^2 (H,(-{\infty},a_1)){\Box}L^2 (H,(a_2,b_2)){\Box}L^2 (H,(a_3,+{\infty})),- {\infty}<a_1<a_2<b_2<a_3<+{\infty} all selfadjoint extensions of the minimal…

We study the pointwise convergence of Landau type Schr\"odinger operators within the fractional Sobolev space $W^{s,p}(\mathbb R)$. Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531-546, 2013) and Yuan, Zhao…

Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…

In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling…

In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems…

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

We study extension operators between spaces $\sigma_n(2^X)$ of subsets of $X$ of cardinality at most $n$. As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$, equipped with the weak topology, then,…

The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…

The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on…

In this paper, we define the fractional Orlicz-Sobolev spaces, and we prove some important results of these spaces. The main result is to show the continuous and compact embedding for these spaces. As an application, we prove the existence…

This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization…

This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…

We prove bounds for multilinear operators on $\R^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true…

In this paper, we give the necessary and sufficient conditions for the boundedness of fractional integral operators on the modulation spaces.

Our aim is to study the modular inequalities for some operators, for example the Bergman projection acting on, in Lebesgue spaces with variable exponent. Under proper assumptions on the variable exponent, we prove that the modular…

We present extensions of rigidity estimates and of Korn's inequality to the setting of (mixed) variable exponents growth. The proof techniques, based on a classical covering argument, rely on the log-H\"older continuity of the exponent to…

In this paper we provide a proof of the Sobolev-Poincar\'e inequality for variable exponent spaces by means of mass transportation methods. The importance of this approach is that the method is exible enough to deal with different…

We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\mathcal{L}_1$ and…