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.
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页码：209 / 223
页数：15
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