On Bernstein- and Marcinkiewicz-type inequalities on multivariate Cα-domains

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2024-09-16 DOI:10.1016/j.jat.2024.106101

引用次数: 0

Abstract

We prove new Bernstein and Markov type inequalities in $L^{p}$ spaces associated with the normal and the tangential derivatives on the boundary of a general compact $C^{α}$ -domain with $1 \leq α \leq 2$ . These estimates are also applied to establish Marcinkiewicz type inequalities for discretization of $L^{p}$ norms of algebraic polynomials on $C^{α}$ -domains with asymptotically optimal number of function samples used.

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论多变量 Cα 域上的伯恩斯坦和马钦凯维奇型不等式

我们证明了 Lp 空间中与 1≤α≤2 的一般紧凑 Cα 域边界上的法导数和切导数相关的新伯恩斯坦和马尔可夫式不等式。这些估计值还被应用于建立 Marcinkiewicz 型不等式，用于 Cα 域上代数多项式 Lp 准则的离散化，并使用渐近最优的函数样本数。

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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