| Title:
|
Some integrability theorems for multiple trigonometric series (English) |
| Author:
|
Lee, Tuo-Yeong |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
269-286 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Several new integrability theorems are proved for multiple cosine or sine series. (English) |
| Keyword:
|
multiple Fourier series |
| Keyword:
|
multiple cosine series |
| Keyword:
|
multiple sine series |
| MSC:
|
40B05 |
| MSC:
|
42B05 |
| idZBL:
|
Zbl 1250.42028 |
| idMR:
|
MR2893976 |
| DOI:
|
10.21136/MB.2011.141649 |
| . |
| Date available:
|
2011-09-22T14:57:32Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141649 |
| . |
| Reference:
|
[1] Boas, R. P.: Integrability Theorems for Trigonometric Transforms.Springer, Berlin (1967). Zbl 0145.06804, MR 0219973 |
| Reference:
|
[2] Grafakos, L.: Classical Fourier analysis. Second edition.Graduate Texts in Mathematics 249. Springer (2008). MR 2445437 |
| Reference:
|
[3] Hardy, G. H.: On the convergence of certain multiple series.Proc. Cambridge Philos. Soc. 19 (1916-1919), 86-95. |
| Reference:
|
[4] Lee, Tuo-Yeong: Proof of two conjectures of Móricz on double trigonometric series.J. Math. Anal. Appl. 340 (2008), 53-63. MR 2376137, 10.1016/j.jmaa.2007.08.010 |
| Reference:
|
[5] Lee, Tuo-Yeong: Some convergence theorems for Lebesgue integrals.Analysis (Munich) 28 (2008), 263-268. Zbl 1156.40007, MR 2401157 |
| Reference:
|
[6] Lee, Tuo-Yeong: A measure-theoretic characterization of the Henstock-Kurzweil integral revisited.Czech. Math. J. 58 (2008), 1221-1231. Zbl 1174.26005, MR 2471178, 10.1007/s10587-008-0081-0 |
| Reference:
|
[7] Lee, Tuo-Yeong: Bounded linear functionals on the space of Henstock-Kurzweil integrable functions.Czech. Math. J. 59 (2009), 1005-1017. Zbl 1224.26026, MR 2563573, 10.1007/s10587-009-0070-y |
| Reference:
|
[8] Lee, Tuo-Yeong: Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series.(to appear) in Czech Math. J. |
| Reference:
|
[9] Móricz, F.: On the convergence in a restricted sense of multiple series.Anal. Math. 5 (1979), 135-147. MR 0539321, 10.1007/BF02059384 |
| Reference:
|
[10] Móricz, F.: Some remarks on the notion of regular convergence of multiple series.Acta Math. Hungar. 41 (1983), 161-168. MR 0704536, 10.1007/BF01994074 |
| Reference:
|
[11] Móricz, F.: On the $| C, \alpha >\frac{1}{2}$, $\beta >\frac{1}{2} |$-summability of double orthogonal series.Acta Sci. Math. (Szeged) 48 (1985), 325-338. MR 0810889 |
| Reference:
|
[12] Móricz, F.: Integrability of double lacunary sine series.Proc. Amer. Math. Soc. 110 (1990), 355-364. MR 1021902, 10.1090/S0002-9939-1990-1021902-5 |
| Reference:
|
[13] Móricz, F.: On the integrability of double cosine and sine series I.J. Math. Anal. Appl. 154 (1991), 452-465. MR 1088644, 10.1016/0022-247X(91)90050-A |
| Reference:
|
[14] Zygmund, A.: Trigonometric Series. Vol. I, II. Third edition.With a foreword by Robert A. Fefferman. Cambridge Mathematical Library. Cambridge University Press, Cambridge (2002). MR 1963498 |
| . |
