On the Kolmogorov Theorems on Fourier Series and Conjugate Functions

被引：1

作者：

Filippov, V. I. ^{[1
]}

机构：

[1] Saratov State Social Econ Univ, Ul Radischcheva 89, Saratov 410003, Russia

来源：

RUSSIAN MATHEMATICS | 2012年 / 56卷 / 07期

关键词：

Fourier series; conjugate functions; generalized Orlicz spaces; classes phi(L);

D O I：

10.3103/S1066369X12070031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Fourier series of summable functions from spaces "wider" than L-1. We describe classes phi(L) which contain conjugate functions, where their conjugate Fourier series converge. The obtained results are more general than A. N. Kolmogorov theorems on the convergence of Fourier series in metrics weaker than that of L-1.

引用

页码：18 / 29

页数：12

共 50 条

[21] Application of the absolute Euler method to some series related to Fourier series and its conjugate series
Ray, BK
Sahoo, AK
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 1996, 106 (01): : 13 - 38
[22] Estimate of the approximation of periodic functions by Fourier series
Besov, OV
MATHEMATICAL NOTES, 2006, 79 (5-6) : 726 - 728
[23] On the divergence of Fourier series of functions in several variablesО расходимости рядов Фурье функций многих переменных
L. Gogoladze
V. Tsagareishvili
Analysis Mathematica, 2013, 39 : 163 - 178
[24] Estimate of the approximation of periodic functions by Fourier series
O. V. Besov
Mathematical Notes, 2006, 79 : 726 - 728
[25] On strong summability of fourier series of summable functions
Pachulia N.L.
Ukrainian Mathematical Journal, 2000, 52 (8) : 1264 - 1273
[26] On the divergence of Fourier series of functions in several variables
Gogoladze, L.
Tsagareishvili, V.
ANALYSIS MATHEMATICA, 2013, 39 (03) : 163 - 178
[27] On a general class of trigonometric functions and Fourier series
Pavao, H. Germano
de Oliveira, E. Capelas
INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, 2008, 39 (07) : 961 - 967
[28] Integrability of the majorants of Fourier series and divergence of the Fourier series of functions with restrictions on the integral modulus of continuity
Antonov, NY
MATHEMATICAL NOTES, 2004, 76 (5-6) : 606 - 619
[29] Integrability of the Majorants of Fourier Series and Divergence of the Fourier Series of Functions with Restrictions on the Integral Modulus of Continuity
N. Yu. Antonov
Mathematical Notes, 2004, 76 : 606 - 619
[30] A Variation on Absolute Weighted Mean Summability Factors of Fourier Series and its Conjugate Series
Yildiz, Sebnem
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2020, 38 (05): : 105 - 113

← 1 2 3 4 5 →