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$L^{1}$-convergences; Cesàro means; conjugate Cesàro mean; semi-convex null coefficients; generalized semi-convex null coefficients; Fourier cosine series
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.
[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
[2] Bosanquet L. S.: Note on the Bohr-Hardy theorem. J. London Math. Soc. 17 (1942), 166–173. MR 0007800 | Zbl 0028.14901
[3] Bosanquet L. S.: Note on convergence and summability factors (III). Proc. London Math. Soc. (1949), 482–496. MR 0027872 | Zbl 0032.40402
[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
[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
[6] Kano T.: Coefficients of some trigonometric series. J. Fac. Sci. Shihshu University 3 (1968), 153–162. MR 0271615 | Zbl 0321.42008
[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
[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 1084.42003
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