NIKOL'SKII INEQUALITIES FOR LORENTZ SPACES

被引：34

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

共 7 条

[1]

[Anonymous], 1995, Grad. Texts in Math.

[2] Combinations of multivariate averages [J].

Dai, F ;

Ditzian, Z .

JOURNAL OF APPROXIMATION THEORY, 2004, 131 (02) :268-283

[3] Multivariate polynomial inequalities with respect to doubling weights and A∞ weights [J].

Dai, Feng .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 235 (01) :137-170

[4] Ul'yanov and Nikol'skii-type inequalities [J].

Ditzian, Z ;

Tikhonov, S .

JOURNAL OF APPROXIMATION THEORY, 2005, 133 (01) :100-133

[5]

Lubinsky D.S., 2007, Surveys in Approximation Theory, V3, P1

[6]

Sherstneva L. A., 1984, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., V4, P75

[7] LANDAU-INEQUALITY FOR FUNCTION OF SEVERAL-VARIABLES [J].

TIMOFEEV, VG .

MATHEMATICAL NOTES, 1985, 37 (5-6) :369-377

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