Rate of convergence of double Fourier series of functions of generalized bounded variation

被引：0

作者：

Bera, Rameshbhai Karshanbhai ^{[1
]}

Ghodadra, Bhikha Lila ^{[1
]}

机构：

[1] Maharaja Sayajirao Univ Baroda, Fac Sci, Dept Math, Vadodara 390002, Gujarat, India

来源：

ACTA SCIENTIARUM MATHEMATICARUM | 2022年 / 88卷 / 3-4期

关键词：

double Fourier series; generalized bounded variation; pointwise convergence; rate of convergence;

D O I：

10.1007/s44146-022-00050-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the rate of convergence of the double Fourier series of a function 2 pi-periodic in each variable and of generalized bounded variation is estimated. The result obtained is a generalization of a result of Bojanic and Waterman for a single Fourier series and of a result of F. Moricz and consequently a result of Hardy for a function of two variables.

引用

页码：723 / 737

页数：15

共 50 条

[41] On the Convergence of Block Fourier Series of Functions of Bounded Variation in Two Variables
Telyakovskii, S. A.
[J]. MATHEMATICAL NOTES, 2018, 103 (3-4) : 645 - 648
[42] On the Convergence of Block Fourier Series of Functions of Bounded Variation in Two Variables
S. A. Telyakovskii
[J]. Mathematical Notes, 2018, 103 : 645 - 648
[43] Absolute Convergence of Double Series of Fourier-Haar Coefficients for Functions of Bounded p-Variation
Golubov, B. I.
[J]. RUSSIAN MATHEMATICS, 2012, 56 (06) : 1 - 10
[44] Absolute convergence of double series of Fourier-Haar coefficients for functions of bounded p-variation
B. I. Golubov
[J]. Russian Mathematics, 2012, 56 (6) : 1 - 10
[45] FOURIER SERIES OF FUNCTIONS OF BOUNDED VARIATION
IZUMI, M
IZUMI, SI
[J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1968, 44 (06): : 415 - &
[46] On Fourier series and functions of bounded variation
Young, WH
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1913, 88 (606) : 561 - 568
[47] Absolute convergence of Fourier series of functions of class Lip 1 and of functions of bounded variation
Tsagareishvili, V. Sh.
[J]. IZVESTIYA MATHEMATICS, 2012, 76 (02) : 419 - 429
[48] A New Estimate of Double Fourier Coefficients for Functions of Bounded Generalized Variation
N. A. Zhukovskii
[J]. Moscow University Mathematics Bulletin, 2021, 76 : 145 - 153
[49] A New Estimate of Double Fourier Coefficients for Functions of Bounded Generalized Variation
Zhukovskii, N. A.
[J]. MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2021, 76 (04) : 145 - 153
[50] Complementary spaces and multipliers of double Fourier series for functions of bounded variation
Baron, S
Liflyand, E
Stadtmüller, U
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 250 (02) : 706 - 721

← 1 2 3 4 5 →