Discrete harmonic analysis associated with Jacobi expansions III: The Littlewood–Paley–Stein gk-functions and the Laplace type multipliers

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2023-10-01 DOI:10.1016/j.jat.2023.105940

Alberto Arenas, Óscar Ciaurri, Edgar Labarga

引用次数: 0

Abstract

The research about harmonic analysis associated with Jacobi expansions carried out in Arenas et al. (2020) and Arenas et al. (2022) is continued in this paper. Given the operator $J^{(α, β)} = J^{(α, β)} - I$ , where $J^{(α, β)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we define the corresponding Littlewood–Paley–Stein $g_{k}^{(α, β)}$ -functions associated with it and we prove an equivalence of norms with weights for them. As a consequence, we deduce a result for Laplace type multipliers.

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与Jacobi展开相关的离散调和分析III：Littlewood–Paley–Stein gk函数和拉普拉斯型乘法器

Arenas等人对与Jacobi展开式相关的调和分析进行了研究。（2020）和Arenas等人。（2022）在本文中继续。给定算子J（α，β）=J。因此，我们推导出拉普拉斯型乘法器的一个结果。

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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