# Necessary and sufficient conditions for the ${L}^{1}$-convergence of double Fourier series

Czechoslovak Mathematical Journal (2018)

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

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topKórus, 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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- 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
- 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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