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Title: Some integrability theorems for multiple trigonometric series (English)
Author: Lee, Tuo-Yeong
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 136
Issue: 3
Year: 2011
Pages: 269-286
Summary lang: English
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Category: math
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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
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Date available: 2011-09-22T14:57:32Z
Last updated: 2013-09-22
Stable URL: http://hdl.handle.net/10338.dmlcz/141649
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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
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
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