Related papers: Classic and exotic Besov spaces induced by good gr…

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 note is based on a series of lectures delivered in Kyoto University. This note surveys the homogeneous Besov space $\dot{B}^s_{pq}$ on ${\mathbb R}^n$ with $1 \le p,q \le \infty$ and $s \in {\mathbb R}$ in a rather self-contained…

We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good…

We study (homogeneous and inhomogeneous) anisotropic Besov spaces associated to expansive dilation matrices $A \in {\rm GL}(d,\mathbb{R})$, with the goal of clarifying when two such matrices induce the same scale of Besov spaces. For this…

Let $1\le p<\infty$, $0<q<\infty$ and $\nu$ be a two-sided doubling weight satisfying $$\sup_{0\le r<1}\frac{(1-r)^q}{\int_r^1\nu(t)\,dt}\int_0^r\frac{\nu(s)}{(1-s)^q}\,ds<\infty.$$ The weighted Besov space $\mathcal{B}_{\nu}^{p,q}$…

The paper is concerned with Besov spaces of variable smoothness $B^{\varphi_{0}}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$, in which the norms are defined in terms of convolutions with smooth functions. A relation is found between the spaces…

Inspired by the classical Besov $p$-space ($1<p<\infty$) defined by means of higher-order derivatives on the upper half-plane, we introduce Besov-type spaces on simply connected domains. We study the relation between the geometric…

We give a new description of classical Besov spaces in terms of a new modulus of continuity. Then a similar approach is used to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure.

We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the…

We show that one can characterize the Besov spaces on a smooth compact oriented Riemannian manifold, for the full range of indices, through a knowledge of the size of frame coefficients, using the frames we have constructed in [8].

We establish a new characterization of the homogeneous Besov spaces $\dot{\mathcal B}^{s}_{p,q}(Z)$ with smoothness $s \in (0,1)$ in the setting of doubling metric measure spaces $(Z,d,\mu)$. The characterization is given in terms of a…

We study the Besov-Morrey spaces $ \mathcal{N}^{s}_{u,p,q}(\mathbb{R}^{d}) $ and show that under certain conditions on the parameters these spaces can be characterized in terms of higher-order differences. Furthermore we prove that some of…

In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the $\varphi $-transforms in appropriate sequence spaces and we obtain atomic decompositions for these…

We give intrinsic characterisations for the uniformly localized versions of the Besov spaces $B^{s}_{p,q}({\mathbb R}^n)$, where $p,q\in [1,+\infty]$, and of the Lizorkin-Triebel spaces $F^{s}_{p,q}({\mathbb R}^n)$, where $q\in [1,+\infty]$…

The Grushin spaces, as one of the most important models in the Carnot-Carath\'eodory space, are a class of locally compact and geodesic metric spaces which admit a dilation. Function spaces on Grushin spaces and some related geometric…

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $VB_{p,q}^{\delta,w}(\mathbb{R}^d)$ whose…

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…

In this paper we investigate Besov-Morrey spaces $\mathcal{N}^{s}_{u,p,q}(\Omega)$ and Besov-type spaces $B^{s,\tau}_{p,q}(\Omega)$ of positive smoothness defined on Lipschitz domains $\Omega \subset \mathbb{R}^d$ as well as on…

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…

We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…