Related papers: Sharp embedding results for spaces of smooth funct…

In this paper, we identify the duals of Triebel-Lizorkin spaces of generalized smoothness. In some particular cases these function spaces are just weighted Triebel-Lizorkin spaces. To do these, we will be working at the level of sequence…

We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on…

The Riemann Mapping Theorem states existence of a conformal homeomorphism $\varphi$ of a simply connected plane domain $\Omega\subset\mathbb C$ with non-empty boundary onto the unit disc $\mathbb D\subset \mathbb C$. In the first part of…

We study weighted Sobolev inequalities on open convex cones endowed with $\alpha$-homogeneous weights satisfying a certain concavity condition. We establish a so-called reduction principle for these inequalities and characterize optimal…

In this article, we give probabilistic versions of Sobolev embeddings on any Riemannian manifold $(M,g)$. More precisely, we prove that for natural probability measures on $L^2(M)$, almost every function belong to all spaces $L^p(M)$,…

In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev…

Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show…

We study associate and double associate spaces of two-weighted Sobolev spaces of the first order on real half-line and we show that unlike the notion of duality the associativity is divided into two cases which we call "strong" and "weak"…

In this note we revisit a result in [9], where we established nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of H\"ormander operators of Kolmogorov-type. We provide here a new proof which…

The purpose of this paper is to extend the embedding theorem of Sobolev spaces involving general kernels and we provide a sharp critical exponent in these embeddings. As an application, solutions for equations driven by a general…

We prove density of smooth functions in subspaces of Sobolev- and higher order $BV$-spaces of kind $W^{m,p}(\Omega)\cap L^q(\Omega-D)$ and $BV^m(\Omega)\cap L^q(\Omega-D)$, respectively, where $\Omega\subset\mathbb{R}^n$ ($n\in\mathbb{N}$)…

In this paper we shall give two-sided sharp estimates of Kolmogorov numbers of embeddings of the Besov spaces with dominating mixed smoothness $S^t_{p,q}B((0,1)^d)$ into $ L_{\infty}((0,1)^d)$.

In this paper we obtain order estimates for entropy numbers of embeddings of weighted Sobolev spaces into weighted Lebesgue spaces and of weighted summation operators on trees. Here we consider some critical conditions on the parameters.

Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad…

We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights $w_0,w_1$ are local Muckenhoupt weights in the sense of Rychkov. As a first step we calculate the Calder\'on products of associated sequence…

We study embeddings of Besov-type and Triebel-Lizorkin-type spaces, $id_\tau : {B}_{p_1,q_1}^{s_1,\tau_1}(\Omega) \hookrightarrow {B}_{p_2,q_2}^{s_2,\tau_2}(\Omega)$ and $id_\tau : {F}_{p_1,q_1}^{s_1,\tau_1}(\Omega) \hookrightarrow…

We study linear polynomial approximation of functions in weighted Sobolev spaces $W^r_{p,w}(\mathbb{R}^d)$ of mixed smoothness $r \in \mathbb{N}$, and their optimality in terms of Kolmogorov and linear $n$-widths of the unit ball…

We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian-Sobolev space). Our result covers first-order…

This paper introduces a matrix analog of the Bessel processes, taking values in the closed set $E$ of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are…

We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney's inequality with weights. As a consequence, under a "weak bounded geometry" hypothesis, we improve classical…