Related papers: Variable Triebel-Lizorkin-type spaces

On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel-Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non)triviality under a…

We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…

We give an extension of the theory of relaxation of variational integrals in classical Sobolev spaces to the setting of metric Sobolev spaces. More precisely, we establish a general framework to deal with the problem of finding an integral…

We provide a complete characterization of compactness of Sobolev embeddings of radially symmetric functions on the entire space $\mathbb{R}^n$ in the general framework of rearrangement-invariant function spaces. We avoid any unnecessary…

We obtain sharp embeddings from the Sobolev space $W^{k,2}_0(-1,1)$ into the space $L^1(-1,1)$ and determine the extremal functions. This improves on a previous estimate of the sharp constants of these embeddings due to Kalyabin.

In this article, we introduce classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p(.) that is summable with respect to measure. These classes of…

Embedding theorems for symmetric functions without zero boundary condition have been studied on flat Riemannian manifolds, such as the Euclidean space. However, these theorems have only been established on hyperbolic spaces for functions…

In this article we construct orthonormal bases compatible with bi-variate homogeneous $\alpha$-modulation spaces and the associated spaces of Triebel-Lizorkin type. The construction is based on generating a separable $\alpha$-covering and…

We survey recent classification theorems for expansive matrices that generate the same anisotropic homogeneous Triebel-Lizorkin function space or sequence space. The function spaces are classified precisely by those matrices for which their…

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…

Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ satisfying Gaussian upper bounds on its heat kernels. In this paper we develop the theory of weighted Besov spaces…

The aim of this paper is to prove duality of Triebel-Lizorkin spaces $% F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }$. First, we prove the duality of associated sequence spaces. Then from the so-called $% \varphi $-transform…

We derive basic properties of Triebel-Lizorkin-Lorentz spaces important in the treatment of PDE. For instance, we prove Triebel-Lizorkin-Lorentz spaces to be of class $\mathcal{HT}$, to have property $(\alpha)$, and to admit a multiplier…

In this paper, we establish the equivalence between the Haj{\l}asz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and…

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, we fill a gap in a step of the proof of the local well-posedness part…

In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the…

The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin--Triebel spaces (that contain the $L_p$-Sobolev spaces $H^s_p$ as special cases). The method extends to a proof of the corresponding fact for general…

The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space.…

Let $0<p<\infty$, $0<q\leq\infty$, and $s\in\mathbb{R}$. We introduce a new type of generalized Besov-type spaces $B_{p,q}^{s,\varphi}(\mathbb{R}^d)$ and generalized Triebel-Lizorkin-type spaces $F_{p,q}^{s,\varphi}(\mathbb{R}^d)$, where…

Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized…