Integrability and $L^1$-convergence of Rees-Stanojević sums with generalized semi-convex coefficients of non-integral orders
Archivum mathematicum, Tome 41 (2005) no. 4, pp. 423-437 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 42A20, 42A32
Keywords: $L^{1}$-convergences; Cesàro means; conjugate Cesàro mean; semi-convex null coefficients; generalized semi-convex null coefficients; Fourier cosine series
@article{ARM_2005_41_4_a6,
     author = {Kaur, Kulwinder},
     title = {Integrability and $L^1$-convergence of {Rees-Stanojevi\'c} sums with generalized semi-convex coefficients of non-integral orders},
     journal = {Archivum mathematicum},
     pages = {423--437},
     year = {2005},
     volume = {41},
     number = {4},
     mrnumber = {2195495},
     zbl = {1111.42001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a6/}
}
TY  - JOUR
AU  - Kaur, Kulwinder
TI  - Integrability and $L^1$-convergence of Rees-Stanojević sums with generalized semi-convex coefficients of non-integral orders
JO  - Archivum mathematicum
PY  - 2005
SP  - 423
EP  - 437
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a6/
LA  - en
ID  - ARM_2005_41_4_a6
ER  - 
%0 Journal Article
%A Kaur, Kulwinder
%T Integrability and $L^1$-convergence of Rees-Stanojević sums with generalized semi-convex coefficients of non-integral orders
%J Archivum mathematicum
%D 2005
%P 423-437
%V 41
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a6/
%G en
%F ARM_2005_41_4_a6
Kaur, Kulwinder. Integrability and $L^1$-convergence of Rees-Stanojević sums with generalized semi-convex coefficients of non-integral orders. Archivum mathematicum, Tome 41 (2005) no. 4, pp. 423-437. http://geodesic.mathdoc.fr/item/ARM_2005_41_4_a6/

[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

[2] Bosanquet L. S.: Note on the Bohr-Hardy theorem. J. London Math. Soc. 17 (1942), 166–173. | MR | Zbl

[3] Bosanquet L. S.: Note on convergence and summability factors (III). Proc. London Math. Soc. (1949), 482–496. | MR | Zbl

[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

[5] Garrett J. W., Stanojević Č. V.: On $L^{1}$-convergence of certain cosine sums. Proc. Amer. Math. Soc. 54 (1976), 101–105. | MR

[6] Kano T.: Coefficients of some trigonometric series. J. Fac. Sci. Shihshu University 3 (1968), 153–162. | MR | Zbl

[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

[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.

[9] Young W. H.: On the Fourier series of bounded functions. Proc. London Math. Soc. 12(2) (1913), 41–70.

[10] Zygmund A.: Trigonometric series. Volume 1, Vol. II, Cambridge University Press. | Zbl