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IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2023-11-29 DOI:10.1016/j.jat.2023.106006

Anton Tselishchev

引用次数: 0

摘要

Rubio de Francia证明了任意区间的Littlewood-Paley不等式的单侧版本。本文证明了任意维伦金系统(即循环群无穷积上的函数)上的类似不等式。对这些基团的顺序没有任何假设。

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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Littlewood–Paley–Rubio de Francia inequality for unbounded Vilenkin systems

Rubio de Francia proved the one-sided version of Littlewood–Paley inequality for arbitrary intervals. In this paper, we prove the similar inequality in the context of arbitrary Vilenkin systems (that is, for functions on infinite products of cyclic groups). There are no assumptions on the orders of these groups.

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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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