Related papers: The Haar System in Besov-type Spaces

We give an explicit construction of Haar functions associated to a system of dyadic cubes in a geometrically doubling quasi-metric space equipped with a positive Borel measure, and show that these Haar functions form a basis for $L^p$. Next…

We consider the spaces $A_p(\mathbb T)$ of functions $f$ on the circle $\mathbb T$ such that the sequence of Fourier coefficients $\fu{\f}=\{\fu{\f}(k), ~k \in \mathbb Z\}$ belongs to $l^p, ~1\leq p<2$. The norm on $A_p(\mathbb T)$ is…

Let $f$ be a function on ${\Bbb R}^2$ in the inhomogeneous Besov space $B_{\infty,1}^1({\Bbb R}^2)$. For a pair $(A,B)$ of not necessarily bounded and not necessarily commuting self-adjoint operators, we define the function $f(A,B)$ of $A$…

In this paper we introduce a polynomial frame on the unit sphere $\sph$ of $\mathbb{R}^d$, for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere $\sph$, such as…

In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univariate boundary adapted quarklets to describe univariate…

This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…

In this paper, we study the smoothness of restrictions of Besov functions. It is known that for any $f\in B\_{p,q}^s(\mathbb{R}^N)$ with $q\leq p$ we have $f(\cdot,y)\in B\_{p,q}^s(\mathbb{R}^d)$ for a.e. $y\in \mathbb{R}^{N-d}$. We prove…

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…

In this paper, we provide a proof that functions belonging to Besov spaces $B^{r}_{q,\infty}(\mathbb{R}^N,\mathbb{R}^d)$, $q\in [1,\infty)$, $r\in(0,1)$, satisfy the following formula under a certain condition: \begin{equation}…

We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale $U^{t,s}_p$ of anisotropic Banach spaces, under the conditions -1+1/p<s<-t<0 and -(r-1)+t<s,…

We consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an…

Let $\Omega$ be a smooth bounded domain in $\mathbb R^n$ and u be a measurable function on $\Omega$ such that $|u(x)|=1$ almost everywhere in $\Omega$. Assume that u belongs to the $B^s_{p,q}(\Omega)$ Besov space. We investigate whether…

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…

General permutations acting on the Haar system are investigated. We give a necessary and sufficient condition for permutations to induce an isomorphism on dyadic BMO. Extensions of this characterization to Lipschitz spaces $\lip,…

This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to…

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…

In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the…

We give a complete characterisation of the spaces $\dot{B}^{\alpha}_{p,q}$ and $\dot{F}^{\alpha}_{p,q}$ by using a non-smooth kernel satisfying near minimal conditions. The tools used include a Stromberg-Torchinsky type estimate for certain…

We extend the results in [6] to Besov spaces $B_{p,q}^\alpha$ with $p,q\in[1,\infty]$ and $0<\alpha<1$.

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…