Some integrability theorems for multiple trigonometric series

Tuo-Yeong Lee

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 3, page 269-286
  • ISSN: 0862-7959

Abstract

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Several new integrability theorems are proved for multiple cosine or sine series.

How to cite

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Lee, Tuo-Yeong. "Some integrability theorems for multiple trigonometric series." Mathematica Bohemica 136.3 (2011): 269-286. <http://eudml.org/doc/197210>.

@article{Lee2011,
abstract = {Several new integrability theorems are proved for multiple cosine or sine series.},
author = {Lee, Tuo-Yeong},
journal = {Mathematica Bohemica},
keywords = {multiple Fourier series; multiple cosine series; multiple sine series; multiple cosine series; sine series; regular convergence; integrability theorem},
language = {eng},
number = {3},
pages = {269-286},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some integrability theorems for multiple trigonometric series},
url = {http://eudml.org/doc/197210},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Lee, Tuo-Yeong
TI - Some integrability theorems for multiple trigonometric series
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 3
SP - 269
EP - 286
AB - Several new integrability theorems are proved for multiple cosine or sine series.
LA - eng
KW - multiple Fourier series; multiple cosine series; multiple sine series; multiple cosine series; sine series; regular convergence; integrability theorem
UR - http://eudml.org/doc/197210
ER -

References

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  1. Boas, R. P., Integrability Theorems for Trigonometric Transforms, Springer, Berlin (1967). (1967) Zbl0145.06804MR0219973
  2. Grafakos, L., Classical Fourier analysis. Second edition, Graduate Texts in Mathematics 249. Springer (2008). (2008) MR2445437
  3. Hardy, G. H., On the convergence of certain multiple series, Proc. Cambridge Philos. Soc. 19 (1916-1919), 86-95. (1916) 
  4. Lee, Tuo-Yeong, 10.1016/j.jmaa.2007.08.010, J. Math. Anal. Appl. 340 (2008), 53-63. (2008) MR2376137DOI10.1016/j.jmaa.2007.08.010
  5. Lee, Tuo-Yeong, Some convergence theorems for Lebesgue integrals, Analysis (Munich) 28 (2008), 263-268. (2008) Zbl1156.40007MR2401157
  6. Lee, Tuo-Yeong, 10.1007/s10587-008-0081-0, Czech. Math. J. 58 (2008), 1221-1231. (2008) Zbl1174.26005MR2471178DOI10.1007/s10587-008-0081-0
  7. Lee, Tuo-Yeong, 10.1007/s10587-009-0070-y, Czech. Math. J. 59 (2009), 1005-1017. (2009) Zbl1224.26026MR2563573DOI10.1007/s10587-009-0070-y
  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., 10.1007/BF02059384, Anal. Math. 5 (1979), 135-147. (1979) MR0539321DOI10.1007/BF02059384
  10. Móricz, F., 10.1007/BF01994074, Acta Math. Hungar. 41 (1983), 161-168. (1983) MR0704536DOI10.1007/BF01994074
  11. Móricz, F., On the | C , α > 1 2 , β > 1 2 | -summability of double orthogonal series, Acta Sci. Math. (Szeged) 48 (1985), 325-338. (1985) MR0810889
  12. Móricz, F., 10.1090/S0002-9939-1990-1021902-5, Proc. Amer. Math. Soc. 110 (1990), 355-364. (1990) MR1021902DOI10.1090/S0002-9939-1990-1021902-5
  13. Móricz, F., 10.1016/0022-247X(91)90050-A, J. Math. Anal. Appl. 154 (1991), 452-465. (1991) MR1088644DOI10.1016/0022-247X(91)90050-A
  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). (2002) MR1963498

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