ON THE SIDON INEQUALITY FOR TRIGONOMETRIC POLYNOMIALS

被引：4

作者：

Radomskii, A. O. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Gubkin Str 8, Moscow 119991, Russia

来源：

ST PETERSBURG MATHEMATICAL JOURNAL | 2018年 / 29卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

Trigonometric polynomial; de la Vallee-Poussin kernel; Riesz product;

D O I：

10.1090/spmj/1510

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A lower estimate is established for the uniform norm of a special type trigonometric polynomial in terms of the sum of the L-1-norms of its summands in the case where the sequence of frequencies splits into finitely many lacunary sequences. The result refines theorems known for lacunary sequences and generalizes a result of Kashin and Temlyakov, which in its turn generalizes the classical Sidon inequality.

引用

页码：643 / 656

页数：14

共 19 条

[11] On the possibility of strengthening Sidon-type inequalities
Radomskii, A. O.
[J]. MATHEMATICAL NOTES, 2013, 94 (5-6) : 829 - 833
[12] Radomskii A. O., 2014, THESIS
[13] On the Fourier coefficients of a continuous function with limited fluctuations
Riesz, F
[J]. MATHEMATISCHE ZEITSCHRIFT, 1918, 2 : 312 - 315
[14] The generalisation of a principle under the absolute convergence of the Fourier series with voids
Sidon, S
[J]. MATHEMATISCHE ANNALEN, 1927, 97 : 675 - 676
[15] Sidon S., 1943, ACTA SCI MATH, V10, P206
[16] Steckin S. B., 1956, IZV AKAD NAUK SSSR M, V20, P385
[17] Temlyakov V.N., 1993, Approximation of Periodic Functions
[18] Zygmund A., 1959, Trigonometric series, V1
[19] [No title captured]

← 1 2 →