Quarklet characterizations for Triebel–Lizorkin spaces

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2023-09-09 DOI:10.1016/j.jat.2023.105968

Marc Hovemann , Stephan Dahlke

引用次数: 2

Abstract

In this paper we prove that under some conditions on the parameters the univariate Triebel–Lizorkin spaces $F_{r, q}^{s} (R)$ can be characterized in terms of quarklets. So for functions from Triebel–Lizorkin spaces we obtain a quarkonial decomposition as well as a new equivalent quasi-norm. For that purpose we use quarklets that are constructed by means of biorthogonal compactly supported Cohen–Daubechies–Feauveau spline wavelets, where the primal generator is a cardinal B-spline. Moreover we introduce some sequence spaces apposite to our quarklet system and study their properties. Finally we also obtain a quarklet characterization for the Triebel–Lizorkin–Morrey spaces $E_{u, r, q}^{s} (R)$ .

查看原文本刊更多论文

Triebel–Lizorkin空间的Quarklet刻画

本文证明了在参数的某些条件下，单变量Triebel–Lizorkin空间Fr，qs（R）可以用夸克来刻画。因此，对于来自Triebel–Lizorkin空间的函数，我们得到了一个夸克分解以及一个新的等价拟范数。为此，我们使用通过双正交紧支撑Cohen–Daubechies–Feauveau样条小波构造的夸克集，其中原始生成器是基数B样条。此外，我们还引入了一些与我们的夸克系统相近的序列空间，并研究了它们的性质。最后，我们还得到了Triebel–Lizorkin–Morrey空间Eu，r，qs（r）的夸克列刻画。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.