Related papers: Pointwise and grand maximal function characterizat…

In this article, the authors establish the pointwise characterization of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type via clarifying the relationship among Haj\l asz-Sobolev spaces, Haj\l asz-Besov and Haj\l…

This paper develops a theory of Besov spaces $\dot{\mathbf{B}}^{\sigma}_{p,q} (N)$ and Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\sigma}_{p,q} (N)$ on an arbitrary homogeneous group $N$ for the full range of parameters $p, q \in (0,…

This paper provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces, denoted by $\dot{F}^s_{p,q}(\mathbb{R}^n)$ and $\dot{B}^s_{p,q}(\mathbb{R}^n)$ respectively, in terms of maximal functions of the…

In this paper, the authors establish new characterizations of the recently introduced Besov-type spaces $\dot{B}^{s,\tau}_{p,q}({\mathbb R}^n)$ and Triebel-Lizorkin-type spaces $\dot{F}^{s,\tau}_{p,q}({\mathbb R}^n)$ with $p\in (0,\infty]$,…

We give Littlewood-Paley type characterizations for Besov-Triebel-Lizorkin-type spaces $\mathscr B_{pq}^{s\tau},\mathscr F_{pq}^{s\tau}$ and Besov-Morrey spaces $\mathcal N_{uqp}^s$ on a special Lipschitz domain $\Omega\subset\mathbb R^n$:…

In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new…

In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces $\dot B^s_{p,\,q}$ and Triebel-Lizorkin spaces $\dot F^s_{p,\,q}$ for all $s\in(0,\,1)$ and $p,\,q\in(n/(n+s),\,\infty],$ both in…

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 $\alpha \in \mathbb{R}$…

In this article, using growth functions we introduce generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. We first characterize these spaces, respectively, in terms of the…

We give characterizations for homogeneous and inhomogeneous Besov-Lizorkin-Triebel spaces in terms of continuous local means for the full range of parameters. In particular, we prove characterizations in terms of Lusin functions and spaces…

Let $s\in{\mathbb R}$, $q\in (0,\infty]$, and $\tau\in[0,\infty)$. It is well known that Besov-type spaces $\dot B^{s,\tau}_{p,q}$ with $p\in (0,\infty]$ and Triebel--Lizorkin-type spaces $\dot F^{s,\tau}_{p,q}$ with $p\in (0,\infty)$ when…

On a general Lie group $G$ endowed with a sub-Riemannian structure and of local dimension $d$, we characterize the pointwise multipliers of Triebel--Lizorkin spaces $F^{p,q}_{\alpha}$ for $p,q\in (1,\infty)$ and $\alpha>d/p$, and those of…

Let $p\in(1,\infty)$, $q\in[1,\infty)$, $s\in\mathbb{R}$ and $\tau\in[0, 1-\frac{1}{\max\{p,q\}}]$. In this paper, the authors establish the $\varphi$-transform characterizations of Besov-Hausdorff spaces $B{\dot…

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 article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of…

In this article, the authors introduce the spaces of Lipschitz type on spaces of homogeneous type in the sense of Coifman and Weiss, and discuss their relations with Besov and Triebel-Lizorkin spaces. As an application, the authors…

Let $(M,\rho,\mu)$ be a metric measure space satisfying the doubling, reverse doubling and non-collapsing conditions, and $\mathscr{L}$ be a self-adjoint operator on $L^2 (M, d\mu)$ whose heat kernel $p_t (x,y)$ satisfy the small-time…

In this article, for an optimal range of the smoothness parameter $s$ that depends (quantitatively) on the geometric makeup of the underlying space, the authors identify purely measure theoretic conditions that fully characterize embedding…

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…

In this article, the authors establish the wavelet characterization of Besov and Triebel--Lizorkin spaces on a given space $(X,d,\mu)$ of homogeneous type in the sense of Coifman and Weiss. Moreover, the authors introduce almost diagonal…