Cesaro Means of Orthogonal Expansions in Several Variables

被引：15

作者：

Dai, Feng ^{[1
]}

Xu, Yuan ^{[2
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

CONSTRUCTIVE APPROXIMATION | 2009年 / 29卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Cesaro means; h-Harmonics; Sphere; Orthogonal polynomials; Ball; Simplex; POLYNOMIALS; SPHERES;

D O I：

10.1007/s00365-008-9008-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Cesaro ( C, delta) means are studied for orthogonal expansions with respect to the weight function Pi(d)(i=1) |x(i)|(2 kappa i) on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp pointwise estimate is established for the ( C, delta) kernel with delta > -1 and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Cesaro means and the projection operator on these domains.

引用

页码：129 / 155

页数：27

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