| Title:
|
Necessary and sufficient conditions for the $L^1$-convergence of double Fourier series (English) |
| Author:
|
Kórus, Péter |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
987-996 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the $L^1$-convergence of double Fourier series. We also give necessary and sufficient conditions for the $L^1$-convergence under appropriate assumptions. (English) |
| Keyword:
|
double Fourier series |
| Keyword:
|
$L^1$-convergence |
| Keyword:
|
logarithm bound variation double sequences |
| MSC:
|
42B05 |
| MSC:
|
42B99 |
| idZBL:
|
Zbl 07031691 |
| idMR:
|
MR3881890 |
| DOI:
|
10.21136/CMJ.2018.0043-17 |
| . |
| Date available:
|
2018-12-07T06:18:47Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147515 |
| . |
| Reference:
|
[1] Belov, A. S.: Remarks on the convergence (boundedness) in the mean of partial sums of a trigonometric series.Math. Notes 71 (2002), 739-748. English. Russian original translation from Mat. Zametki 71 2002 807-817. Zbl 1026.42010, MR 1933102, 10.1023/A:1015860510199 |
| Reference:
|
[2] He, J. L., Zhou, S. P.: On $L^1$-convergence of double sine series.Acta Math. Hung. 143 (2014), 107-118. Zbl 1324.42011, MR 3215608, 10.1007/s10474-013-0376-y |
| Reference:
|
[3] Kaur, K., Bhatia, S. S., Ram, B.: $L^1$-convergence of complex double Fourier series.Proc. Indian Acad. Sci., Math. Sci. 113 (2003), 355-363. Zbl 1041.42005, MR 2020071, 10.1007/BF02829630 |
| Reference:
|
[4] Móricz, F.: Necessary conditions for $L^1$-convergence of double Fourier series.J. Math. Anal. Appl. 363 (2010), 559-568. Zbl 1182.42009, MR 2564875, 10.1016/j.jmaa.2009.09.030 |
| Reference:
|
[5] Tikhonov, S.: On $L_1$-convergence of Fourier series.J. Math. Anal. Appl. 347 (2008), 416-427. Zbl 1257.42009, MR 2440338, 10.1016/j.jmaa.2008.05.048 |
| Reference:
|
[6] Zhou, S. P.: What condition can correctly generalize monotonicity in $L^1$-convergence of sine series?.Sci. Sin., Math. 40 (2010), 801-812 Chinese. MR 3051121 |
| . |
