Relations between Kondratiev spaces and refined localization Triebel–Lizorkin spaces

IF 0.6 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2025-03-18 DOI:10.1016/j.jat.2025.106162

Markus Hansen , Benjamin Scharf, Cornelia Schneider

引用次数: 0

Abstract

We investigate the close relation between certain weighted Sobolev spaces (Kondratiev spaces) and refined localization spaces from Triebel (2006), Triebel (2008). In particular, using a characterization for refined localization spaces from Scharf (2014), we considerably improve an embedding from Hansen (2013). This embedding is of special interest in connection with convergence rates for adaptive approximation schemes.

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Kondratiev空间与精细定位triiebel - lizorkin空间的关系

我们从triiebel (2006), triiebel（2008）中研究了某些加权Sobolev空间（Kondratiev空间）与精细定位空间之间的密切关系。特别是，使用Scharf（2014）的精细定位空间表征，我们大大改进了Hansen（2013）的嵌入。这种嵌入与自适应近似方案的收敛速率有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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