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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1112–1122 (Mi izv2507)  

This article is cited in 13 scientific papers (total in 13 papers)

A generalization of a theorem of Marcinkiewicz

L. V. Zhizhiashvili


Abstract: It is proved that a double Fourier series is $(C,\alpha)$-summable with $\alpha>0$ almost everywhere.

Full text: PDF file (717 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1065–1075

Bibliographic databases:

UDC: 517.5
MSC: 42B05, 42B08, 40G05, 26B25
Received: 20.11.1967

Citation: L. V. Zhizhiashvili, “A generalization of a theorem of Marcinkiewicz”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1112–1122; Math. USSR-Izv., 2:5 (1968), 1065–1075

Citation in format AMSBIB
\Bibitem{Zhi68}
\by L.~V.~Zhizhiashvili
\paper A generalization of a theorem of Marcinkiewicz
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 5
\pages 1112--1122
\mathnet{http://mi.mathnet.ru/izv2507}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=234212}
\zmath{https://zbmath.org/?q=an:0174.36002|0183.33203}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1065--1075
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000702}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127  mathnet  crossref  mathscinet  zmath
    2. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. D. Nakhman, “Lebesgue constants of arithmetic means of double Fourier–Legendre sums”, Russian Math. (Iz. VUZ), 43:8 (1999), 34–43  mathnet  mathscinet  zmath  elib
    4. Ferenc Weisz, “A Generalization for Fourier Transforms of a Theorem due to Marcinkiewicz”, Journal of Mathematical Analysis and Applications, 252:2 (2000), 675  crossref
    5. Hubert Berens, Zhongkai Li, Yuan Xu, “On l-1 Riesz summability of the inverse Fourier integral”, Indagationes Mathematicae, 12:1 (2001), 41  crossref
    6. Ferenc Weisz, “Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series”, Journal of Mathematical Analysis and Applications, 2011  crossref
    7. Ushangi Goginava, Ferenc Weisz, “Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series”, Studia Scientiarum Mathematicarum Hungarica, 49:2 (2012), 236  crossref
    8. Ferenc Weisz, “Lebesgue Points of Two-Dimensional Fourier Transforms and Strong Summability”, J Fourier Anal Appl, 2015  crossref
    9. Ferenc Weisz, “Lebesgue Points of Two-Dimensional Fourier Transforms and Strong Summability”, J Fourier Anal Appl, 2015  crossref
    10. Ferenc Weisz, “Lebesgue points of double Fourier series and strong summability”, Journal of Mathematical Analysis and Applications, 2015  crossref
    11. Goginava U., “Almost Everywhere Strong Summability of Cubic Partial Sums of D-Dimensional Walsh-Fourier Series”, Math. Inequal. Appl., 20:4 (2017), 1051–1066  crossref  isi
    12. Weisz F., “Convergence and Summability of Fourier Transforms and Hardy Spaces”, Convergence and Summability of Fourier Transforms and Hardy Spaces, Applied and Numerical Harmonic Analysis, Birkhauser Boston, 2017, 1–435  crossref  isi
    13. G. A. Karagulyan, H. Mkoyan, “An exponential estimate for the cubic partial sums of multiple Fourier series”, Izv. Math., 83:2 (2019), 273–286  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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