Necessary and sufficient conditions for the L 1 -convergence of double Fourier series

Péter Kórus

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 4, page 987-996
  • ISSN: 0011-4642

Abstract

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We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the L 1 -convergence of double Fourier series. We also give necessary and sufficient conditions for the L 1 -convergence under appropriate assumptions.

How to cite

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Kórus, Péter. "Necessary and sufficient conditions for the $L^1$-convergence of double Fourier series." Czechoslovak Mathematical Journal 68.4 (2018): 987-996. <http://eudml.org/doc/294766>.

@article{Kórus2018,
abstract = {We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the $L^1$-convergence of double Fourier series. We also give necessary and sufficient conditions for the $L^1$-convergence under appropriate assumptions.},
author = {Kórus, Péter},
journal = {Czechoslovak Mathematical Journal},
keywords = {double Fourier series; $L^1$-convergence; logarithm bound variation double sequences},
language = {eng},
number = {4},
pages = {987-996},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Necessary and sufficient conditions for the $L^1$-convergence of double Fourier series},
url = {http://eudml.org/doc/294766},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Kórus, Péter
TI - Necessary and sufficient conditions for the $L^1$-convergence of double Fourier series
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 987
EP - 996
AB - We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the $L^1$-convergence of double Fourier series. We also give necessary and sufficient conditions for the $L^1$-convergence under appropriate assumptions.
LA - eng
KW - double Fourier series; $L^1$-convergence; logarithm bound variation double sequences
UR - http://eudml.org/doc/294766
ER -

References

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  1. Belov, A. S., 10.1023/A:1015860510199, Math. Notes 71 (2002), 739-748. English. Russian original translation from Mat. Zametki 71 2002 807-817. (2002) Zbl1026.42010MR1933102DOI10.1023/A:1015860510199
  2. He, J. L., Zhou, S. P., 10.1007/s10474-013-0376-y, Acta Math. Hung. 143 (2014), 107-118. (2014) Zbl1324.42011MR3215608DOI10.1007/s10474-013-0376-y
  3. Kaur, K., Bhatia, S. S., Ram, B., 10.1007/BF02829630, Proc. Indian Acad. Sci., Math. Sci. 113 (2003), 355-363. (2003) Zbl1041.42005MR2020071DOI10.1007/BF02829630
  4. Móricz, F., 10.1016/j.jmaa.2009.09.030, J. Math. Anal. Appl. 363 (2010), 559-568. (2010) Zbl1182.42009MR2564875DOI10.1016/j.jmaa.2009.09.030
  5. Tikhonov, S., 10.1016/j.jmaa.2008.05.048, J. Math. Anal. Appl. 347 (2008), 416-427. (2008) Zbl1257.42009MR2440338DOI10.1016/j.jmaa.2008.05.048
  6. Zhou, S. P., What condition can correctly generalize monotonicity in L 1 -convergence of sine series?, Sci. Sin., Math. 40 (2010), 801-812 Chinese. (2010) 

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