NIKOL'SKII INEQUALITIES FOR LORENTZ SPACES

被引：30

作者：

Ditzian, Z. ^{[1
]}

Prymak, A. ^{[2
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2T1, Canada

[2] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2010年 / 40卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1216/RMJ-2010-40-1-209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A general approach is given for establishing Nikol'skii-type inequalities for various Lorentz spaces. The key ingredient for the proof is either a Bernstein-type inequality or a Remez-type inequality. Applications of our results to trigonometric polynomials on the torus T(d), algebraic polynomials on [-1, 1], spherical harmonic polynomials on the unit sphere S(d-1) in R(d), algebraic polynomials on R with Freud's weights and others will be presented.

引用

页码：209 / 223

页数：15

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