单纯形上的锐伯恩斯坦不等式

IF 2.3 2区数学 Q1 MATHEMATICS

Constructive Approximation Pub Date : 2024-02-24 DOI:10.1007/s00365-024-09680-6

Yan Ge, Yuan Xu

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引用次数: 0

摘要

我们证明了简单面上两类伯恩斯坦不等式的几个新系列。第一类是雅可比权重的 \(L^2\) norm 不等式，其中一些是尖锐的，它们是通过以正交多项式为特征函数的谱算子建立的。第二种类型包括单纯形上加倍权重的 \(L^p\) norm 不等式。当 \(d \ge 3\) 时，第一类不一定是第二类的特例。

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Sharp Bernstein Inequalities on Simplex

We prove several new families of Bernstein inequalities of two types on the simplex. The first type consists of inequalities in \(L^2\) norm for the Jacobi weight, some of which are sharp, and they are established via the spectral operator that has orthogonal polynomials as eigenfunctions. The second type consists of inequalities in \(L^p\) norm for doubling weight on the simplex. The first type is not necessarily a special case of the second type when \(d \ge 3\).

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来源期刊

Constructive Approximation 数学-数学

CiteScore

3.50

自引率

3.70%

发文量

审稿时长

1 months

期刊介绍： Constructive Approximation is an international mathematics journal dedicated to Approximations and Expansions and related research in computation, function theory, functional analysis, interpolation spaces and interpolation of operators, numerical analysis, space of functions, special functions, and applications.