Related papers: Quarklet Characterizations for Triebel-Lizorkin Sp…

This is a contribution to the theory of Lizorkin--Triebel spaces having mixed Lebesgue norms and quasi-homogeneous smoothness. We discuss their characterisation in terms of general quasi-norms based on convolutions. In particular, this…

This paper provides maximal function characterizations of anisotropic Triebel-Lizorkin spaces associated to general expansive matrices for the full range of parameters $p \in (0,\infty)$, $q \in (0,\infty]$ and $\alpha \in \mathbb{R}$. The…

Given any uniform domain $\Omega$, the Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ with $0<s<1$ and $1<p,q<\infty$ can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to…

We construct smooth localized orthonormal bases compatible with homogeneous mixed-norm Triebel-Lizorkin spaces in an anisotropic setting on $\bR^d$. The construction is based on tensor products of so-called univariate brushlet functions…

Under certain restrictions on $s,p,q$, the Triebel-Lizorkin spaces can be viewed as generalised fractional Sobolev spaces $W^{s,p}_q$. In this article, we show that the Bourgain-Brezis-Mironescu formula holds for $W^{s,p}_q$-seminorms in…

In this paper we study Triebel-Lizorkin-type spaces with variable smoothness and integrability. We show that our space is well-defined, i.e., independent of the choice of basis functions and we obtain their atomic characterization. Moreover…

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 establish Triebel-Lizorkin spaces in the Dunkl setting which are associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent metrics: the Euclidean metric and the Dunkl metric. In this…

In this paper, the author introduce Triebel-Lizorkin spaces with general smoothness. We present the $\varphi $-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. Also, we…

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…

In this paper, we introduce a new family of function spaces of Besov and Triebel-Lizorkin type. We present the $\varphi $-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and…

In this paper we develop a theory of Besov and Triebel--Lizorkin spaces on general noncompact Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means of hypoelliptic sub-Laplacians with drift, and endowed with a…

Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\alpha}_{p,q}$ for the endpoint case of $p = \infty$ and the full scale of parameters $\alpha \in \mathbb{R}$…

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel--Lizorkin-type spaces $\dot B^{s,\tau}_{p,q}(W)$ and $\dot F^{s,\tau}_{p,q}(W)$. In this article, the authors establish the molecular…

Let $L$ be the Dunkl Laplacian on the Euclidean space $\mathbb{R}^N$ associated with a normalized root system $R$ and a multiplicity function $k(\nu)\geq 0$, $\nu\in R$. We establish a Leibniz-type rule for the fractional powers of $L$ on…

In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of…

We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets, on bisimplicial spaces, on bisimplicial sets, on marked simplicial spaces. The main…

We obtain asymptotically sharp identification of fractional Sobolev spaces $ W^{s}_{p,q}$, extension spaces $E^{s}_{p,q}$, and Triebel-Lizorkin spaces $\dot{F}^s_{p,q}$. In particular we obtain for $W^{s}_{p,q}$ and $E^{s}_{p,q}$ a…

We discuss the growth envelopes of Fourier-analytically defined Besov and Triebel-Lizorkin spaces $B^s_{p,q}(\R^n)$ and $F^s_{p,q}(\R^n)$ for $s=\sigma_p=n\max(\frac 1p-1,0)$. These results may be also reformulated as optimal embeddings…