| Title:
|
Integrability and $L^1$-convergence of Rees-Stanojević sums with generalized semi-convex coefficients of non-integral orders (English) |
| Author:
|
Kaur, Kulwinder |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
423-437 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Integrability and $L^{1}-$convergence of modified cosine sums introduced by Rees and Stanojević under a class of generalized semi-convex null coefficients are studied by using Cesàro means of non-integral orders. (English) |
| Keyword:
|
$L^{1}$-convergences |
| Keyword:
|
Cesàro means |
| Keyword:
|
conjugate Cesàro mean |
| Keyword:
|
semi-convex null coefficients |
| Keyword:
|
generalized semi-convex null coefficients |
| Keyword:
|
Fourier cosine series |
| MSC:
|
42A20 |
| MSC:
|
42A32 |
| idZBL:
|
Zbl 1111.42001 |
| idMR:
|
MR2195495 |
| . |
| Date available:
|
2008-06-06T22:46:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107971 |
| . |
| Reference:
|
[1] Andersen A. F.: On extensions within the theory of Cesàro summability of a classical convergence theorem of Dedekind.Proc. London Math. Soc. 8 (1958), 1–52. MR 0092880 |
| Reference:
|
[2] Bosanquet L. S.: Note on the Bohr-Hardy theorem.J. London Math. Soc. 17 (1942), 166–173. Zbl 0028.14901, MR 0007800 |
| Reference:
|
[3] Bosanquet L. S.: Note on convergence and summability factors (III).Proc. London Math. Soc. (1949), 482–496. Zbl 0032.40402, MR 0027872 |
| Reference:
|
[4] Garrett J. W., Stanojević Č. V.: On integrability and $L^{1}$-convergence of certain cosine sums.Notices, Amer. Math. Soc. 22 (1975), A–166. MR 2625039 |
| Reference:
|
[5] Garrett J. W., Stanojević Č. V.: On $L^{1}$-convergence of certain cosine sums.Proc. Amer. Math. Soc. 54 (1976), 101–105. MR 0394002 |
| Reference:
|
[6] Kano T.: Coefficients of some trigonometric series.J. Fac. Sci. Shihshu University 3 (1968), 153–162. Zbl 0321.42008, MR 0271615 |
| Reference:
|
[7] Kaur K., Bhatia S. S.: Integrability and L-convergence of Rees-Stanojević sums with generalized semi-convex coefficients.Int. J. Math. Math. Sci. 30(11) (2002), 645–650. MR 1916824 |
| Reference:
|
[8] Kolmogorov A. N.: Sur l’ordere de grandeur des coefficients de la series de Fourier–Lebesque.Bull. Polon. Sci. Ser. Sci. Math. Astronom. Phys. (1923) 83–86. |
| Reference:
|
[9] Young W. H.: On the Fourier series of bounded functions.Proc. London Math. Soc. 12(2) (1913), 41–70. |
| Reference:
|
[10] Zygmund A.: Trigonometric series.Volume 1, Vol. II, Cambridge University Press. Zbl 1084.42003 |
| . |
