Related papers: A classification of anisotropic Besov spaces
We give several characterizations of holomorphic mean Besov-Lipschitz space on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz space involve…
In this paper, we introduce a class of homeomorphisms between metric spaces, which are locally biH\"{o}lder continuous mappings. Then an embedding result between Besov spaces induced by locally biH\"{o}lder continuous mappings between…
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…
We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using…
In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces…
It is shown that para-multiplication applies to a certain product $\pi(u,v)$ defined for appropriate temperate distributions $u$ and $v$. Boundedness of $\pi(\cdot,\cdot)$ is investigated for the anisotropic Besov and Triebel--Lizorkin…
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
In this work we establish a sampling theorem for functions in Besov spaces on spaces of homogeneous type as defined in [HY] in the spirit of their recent counterpart for R d established by Jaming-Malinnikova in [JM]. The main tool is the…
Whether embedding spaces use all their dimensions equally, i.e., whether they are isotropic, has been a recent subject of discussion. Evidence has been accrued both for and against enforcing isotropy in embedding spaces. In the present…
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $\mathbb{T}^d_\theta$ (with $\theta$ a skew symmetric real $d\times d$-matrix). These spaces share many properties with their…
In this paper we prove Nikolskii's inequality on general compact Lie groups and on compact homogeneous spaces with the constant interpreted in terms of the eigenvalue counting function of the Laplacian on the space, giving the best constant…
In this article, using variable matrix ${\mathscr{A}}_{p(\cdot),\infty}$ weights, we introduce the matrix-weighted variable Besov space $B^{s(\cdot)}_{p(\cdot),q(\cdot)}(W)$ and the corresponding averaging variable Besov space…
In this article, we study the relation between Sobolev-type embeddings for Sobolev spaces or Besov spaces or Triebel-Lizorkin spaces defined either on a doubling or on a geodesic metric measure space and lower bound for measure of balls…
In this paper we investigate Besov spaces on graded Lie groups. We prove a Nikolskii type inequality (or the Reverse H\"older inequality) on graded Lie groups and as consequence we obtain embeddings of Besov spaces. We prove a version of…
We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces $Z$. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices $s<1,$ as well as the first order…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
We study compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces with variable exponents on both bounded and unbounded metric measure spaces. We establish sufficient conditions for compactness, and under additional assumptions, we…
In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…
Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this paper we develop an embedding theory for variable…
We study the behavior of Haar coefficients in Besov and Triebel-Lizorkin spaces on $\mathbb{R}$, for a parameter range in which the Haar system is not an unconditional basis. First, we obtain a range of parameters, extending up to…