On the Growth Rate of Arbitrary Sequences of Double Rectangular Fourier Sums

被引：1

作者：

Antonov, N. Yu. ^{[1
]}

机构：

[1] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620990, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2011年 / 273卷

基金：

俄罗斯基础研究基金会;

关键词：

multiple trigonometric Fourier series; almost everywhere convergence; SERIES; CONVERGENCE;

D O I：

10.1134/S0081543811050026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theorem is proved that an arbitrary sequence {S-mk,S-nk(f, x, y)}(k=1)(infinity) of double rectangular Fourier sums of any function from the class L(ln(+) L)(2)([0, 2 pi)(2)) satisfies the relation S-mk,S-nk (f, x, y) = o(ln k) almost everywhere.

引用

页码：S14 / S20

页数：7

共 31 条

[1] On the growth rate of arbitrary sequences of double rectangular Fourier sums
N. Yu. Antonov
Proceedings of the Steklov Institute of Mathematics, 2011, 273 : 14 - 20
[2] On the growth rate of arbitrary sequences of double rectangular Fourier sums
Antonov, N. Yu.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2010, 16 (04): : 31 - 37
[3] Growth Estimates for Arbitrary Sequences of Multiple Rectangular Fourier Sums
Antonov, N. Yu
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2014, 284 : S1 - S8
[4] A note on estimates for the growth order of sequences of multiple rectangular Fourier sums
Antonov, N. Yu
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2012, 277 : 4 - 8
[5] On the Almost Everywhere Convergence of Sequences of Multiple Rectangular Fourier Sums
Antonov, N. Yu.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2009, 264 : 1 - 18
[6] On the growth order of sequences of double rectangular Fourier sums for functions from the classes phi(L)
Antonov, N. Yu.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2012, 18 (04): : 26 - 34
[7] Note on estimates for the growth order of sequences of multiple rectangular Fourier sums
Antonov, N. Y.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2011, 17 (03): : 55 - 59
[8] A note on estimates for the growth order of sequences of multiple rectangular Fourier sums
N. Yu. Antonov
Proceedings of the Steklov Institute of Mathematics, 2012, 277 : 4 - 8
[9] On the almost everywhere convergence of sequences of multiple rectangular Fourier sums
N. Yu. Antonov
Proceedings of the Steklov Institute of Mathematics, 2009, 264 : 1 - 18
[10] On almost everywhere convergence of lacunary sequences of multiple rectangular Fourier sums
N. Yu. Antonov
Proceedings of the Steklov Institute of Mathematics, 2017, 296 : 43 - 59

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