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Keywords:
multiple Fourier series; multiple cosine series; multiple sine series
multiple Fourier series; multiple cosine series; multiple sine series
Summary:
Several new integrability theorems are proved for multiple cosine or sine series.
References:
[1] Boas, R. P.: Integrability Theorems for Trigonometric Transforms. Springer, Berlin (1967). MR 0219973 | Zbl 0145.06804
[2] Grafakos, L.: Classical Fourier analysis. Second edition. Graduate Texts in Mathematics 249. Springer (2008). MR 2445437
[3] Hardy, G. H.: On the convergence of certain multiple series. Proc. Cambridge Philos. Soc. 19 (1916-1919), 86-95.
[4] Lee, Tuo-Yeong: Proof of two conjectures of Móricz on double trigonometric series. J. Math. Anal. Appl. 340 (2008), 53-63. DOI 10.1016/j.jmaa.2007.08.010 | MR 2376137
[5] Lee, Tuo-Yeong: Some convergence theorems for Lebesgue integrals. Analysis (Munich) 28 (2008), 263-268. MR 2401157 | Zbl 1156.40007
[6] Lee, Tuo-Yeong: A measure-theoretic characterization of the Henstock-Kurzweil integral revisited. Czech. Math. J. 58 (2008), 1221-1231. DOI 10.1007/s10587-008-0081-0 | MR 2471178 | Zbl 1174.26005
[7] Lee, Tuo-Yeong: Bounded linear functionals on the space of Henstock-Kurzweil integrable functions. Czech. Math. J. 59 (2009), 1005-1017. DOI 10.1007/s10587-009-0070-y | MR 2563573 | Zbl 1224.26026
[8] Lee, Tuo-Yeong: Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series. (to appear) in Czech Math. J.
[9] Móricz, F.: On the convergence in a restricted sense of multiple series. Anal. Math. 5 (1979), 135-147. DOI 10.1007/BF02059384 | MR 0539321
[10] Móricz, F.: Some remarks on the notion of regular convergence of multiple series. Acta Math. Hungar. 41 (1983), 161-168. DOI 10.1007/BF01994074 | MR 0704536
[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
[12] Móricz, F.: Integrability of double lacunary sine series. Proc. Amer. Math. Soc. 110 (1990), 355-364. DOI 10.1090/S0002-9939-1990-1021902-5 | MR 1021902
[13] Móricz, F.: On the integrability of double cosine and sine series I. J. Math. Anal. Appl. 154 (1991), 452-465. DOI 10.1016/0022-247X(91)90050-A | MR 1088644
[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
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