Related papers: HK-Sobolev space $W{S^{k,p}}$ on $\mathbb{R}^\inft…

In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional…

The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of…

The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schr\"odinger equation…

In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional…

Verifying lower-semicontinuity of integral functionals in the weak topology of Sobolev spaces is a central theme in the calculus of variations. For integral functionals with $p$-growth, quasiconvexity is a necessary condition for weak…

We describe some sufficient conditions, under which smooth and compactly supported functions are or are not dense in the fractional Sobolev space $W^{s,p}(\Omega)$ for an open, bounded set $\Omega\subset\mathbb{R}^{d}$. The density property…

In this paper, we define weighted relative $p(.)$-capacity and discuss properties of capacity in the space $W_{\vartheta }^{1,p(.)}(\mathbb{R}^{n}).$ Also, we investigate some properties of weighted variable Sobolev capacity. It is shown…

The main goal of this paper is to introduce a new fractional anisotropic Sobolev space with variable exponent where the basic qualitative properties (completeness, separability, reflexivity, ...) are established, including the continuous…

We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvment of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin type estimates of…

We focus on the Sobolev spaces of bounded subanalytic submanifolds of $\mathbb{R}^n$. We prove that if $M$ is such a manifold then the space $\mathscr{C}_0^\infty(M)$ is dense in $W^{1,p}(M,\partial M)$ (the kernel of the trace operator)…

We prove the Lp,q-solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces with the lowest integrability conditions. In particular, the…

We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the…

We prove uniform boundedness of certain boundary representations on appropriate fractional Sobolev spaces $W^{s,p}$ with $p>1$ for arbitrary Gromov hyperbolic groups. These are closed subspaces of $L^p$ and in particular Hilbert spaces in…

In this article, for $N \geq 2, s \in (1,2), p\in (1, \frac{N}{s}), \sigma=s-1 $ and $a \in [0, \frac{N-sp}{2})$, we establish an isometric isomorphism between the higher order fractional weighted Beppo-Levi space \begin{align*} {\mathcal…

We introduce the Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $0<p<1$, thereby extending earlier constructions for $1\leq p\leq \infty$. We then establish various properties of these spaces,…

We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $\R^d$, equipped with power weights $w(x) = |x|^\gamma$, $\gamma>-d$. We prove two-weight Sobolev embeddings for these spaces. Moreover, we…

The present article is concerned with the nonlinear approximation of functions in the Sobolev space H^q with respect to a tensor-product, or hyperbolic wavelet basis on the unit n-cube. Here, q is a real number, which is not necessarily…

The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation…

We show that in a bounded Gromov hyperbolic domain $\Omega$ smooth functions with bounded derivatives $C^\infty(\Omega)\cap W^{k,\infty}(\Omega)$ are dense in the homogeneous Sobolev spaces $L^{k,p}(\Omega)$.

We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces…