加权氡测量偶的Calderón-Mityagin性质

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2026-03-01 Epub Date: 2025-08-19 DOI:10.1016/j.jat.2025.106224

Per G. Nilsson

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引用次数: 0

摘要

本文的目的是引入两个新的基于连续函数的加权空间和正实数线上的加权Radon测度的泛型Banach格对，分别用C -l和M -l表示。这导致了一种基于这些对的关于加权L1空间Calderón-Mityagin性质的Sedaev-Semenov结果的新方法。由此得到了K可分性的概念与M - l和一般Banach对的Calderón-Mityagin性质之间的形式等价。

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The Calderón–Mityagin property for couples of weighted Radon measures

The aim of this note is to introduce two new generic Banach lattice couples based on weighted spaces of continuous functions, and weighted Radon measures on the positive real-line, denoted by

\vec{C}

and

\vec{M}

respectively. This leads to a new approach, based on these couples, of the Sedaev–Semenov result regarding the Calderón–Mityagin property for weighted

L_{1}

spaces. As a consequence is obtained a formal equivalence between the concept of

K

divisibility and the relative Calderón–Mityagin Property between

\vec{M}

and general Banach couples.

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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.