Related papers: Wavelets in function spaces on cellular domains

Recently Gigli developed a Sobolev calculus on non-smooth spaces using module theory. In this paper it is shown that his theory fits nicely into the theory of differentiability spaces initiated by Cheeger, Keith and others. A relaxation…

We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the…

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 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,…

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…

This paper is concerned with complex Banach-space valued functions of the form $$ \hat{f}_k(r\cos\theta,r\sin\theta,z)=\mathrm{e}^{\mathrm{i} k \theta}f_k(r,z), \qquad r \in [0,\infty), \theta \in \mathbb{T}^1, z \in \mathbb{R}, $$ for some…

Let $D\in\mathbb{N}$, $q\in[2,\infty)$ and $(\mathbb{R}^D,|\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $\mathrm{WE}^{1,\,q}(\mathbb R^D)$ defined…

We exhibit the necessary range for which functions in the Sobolev spaces $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle-Lemari\'e wavelets. We also consider the natural…

In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…

This paper is devoted to the question of constructing a higher order Faber spline basis for the sampling discretization of functions with higher regularity than Lipschitz. The basis constructed in this paper has similar properties as the…

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

We study the spaces of Besov and Triebel-Lizorkin type with variable smoothness and integrability as introduced recently by Almeida & H\"ast\"o and Diening, H\"ast\"o & Roudenko. Both scales cover many classical spaces with fixed exponents…

We study embeddings between generalised Besov-Morrey spaces. Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces are also considered. Our approach requires a…

We study weighted Besov and Triebel--Lizorkin spaces associated with Hermite expansions and obtain (i) frame decompositions, and (ii) characterizations of continuous Sobolev-type embeddings. The weights we consider generalize the…

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…

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion…

Fractional Sobolev spaces $\widehat{H}^s(\mathbb{R})$ have been playing important roles in analysis of many mathematical subjects. In this work, we re-consider fractional Sobolev spaces under the perspective of fractional operators and…

We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^d$. This covers, in particular, the well-known situation for spaces of Besov and Triebel-Lizorkin…

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly…

Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…