The norm of the Cesàro operator minus the identity and related operators acting on decreasing sequences

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2023-08-01 DOI:10.1016/j.jat.2023.105911

Santiago Boza , Javier Soria

引用次数: 0

Abstract

Recently, several authors have considered the problem of determining optimal norm inequalities for discrete Hardy-type operators (like Cesàro or Copson). In this work, we obtain sharp bounds for the norms of the difference of the Cesàro operator with either the identity or the shift, when they are restricted to the cone of decreasing sequences in $ℓ^{p}$ (which is closely related to the previously mentioned estimates). Finally, we also address the case of weighted inequalities and find an interesting contrast between the norms of these two difference operators.

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Cesàro算子的范数减去作用于递减序列的恒等式和相关算子

最近，一些作者考虑了离散Hardy型算子（如Cesàro或Copson）的最优范数不等式的确定问题。在这项工作中，当Cesàro算子的差分范数被限制在ℓp（这与前面提到的估计密切相关）。最后，我们还讨论了加权不等式的情况，并发现这两个差分算子的范数之间存在有趣的对比。

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.