RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 4, Pages 937–958 (Mi izv1874)  

This article is cited in 4 scientific papers (total in 4 papers)

On $(H,k)$-summability of multiple trigonometric Fourier series

L. D. Gogoladze


Abstract: A theorem is proved from which, in particular, it follows that if $f\in L(\ln^+L)^{N-1}$ on $T^N\equiv[-\pi,\pi]^N$, then the multiple trigonometric Fourier series of $f$ and all conjugate series are $(H,k)$-summable almost everywhere on $T^N$ for every $k>0$.
In the case where $f\in L(\ln^+L)^{N+1}$ this result was obtained by Marcinkiewicz (Collected papers, PWN, Warsaw, 1964).
That it is unimprovable, in a certain sense, follows from a result of Saks (On the strong derivatives of functions of intervals, Fund. Math. 25 (1935), 235–252).
Bibliography: 15 titles.

Full text: PDF file (1342 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1977, 11:4, 889–908

Bibliographic databases:

UDC: 517.5
MSC: 42A24, 42A92, 42A40, 40G05
Received: 05.01.1976

Citation: L. D. Gogoladze, “On $(H,k)$-summability of multiple trigonometric Fourier series”, Izv. Akad. Nauk SSSR Ser. Mat., 41:4 (1977), 937–958; Math. USSR-Izv., 11:4 (1977), 889–908

Citation in format AMSBIB
\Bibitem{Gog77}
\by L.~D.~Gogoladze
\paper On $(H,k)$-summability of multiple trigonometric Fourier series
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 4
\pages 937--958
\mathnet{http://mi.mathnet.ru/izv1874}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473711}
\zmath{https://zbmath.org/?q=an:0362.42003}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 4
\pages 889--908
\crossref{https://doi.org/10.1070/IM1977v011n04ABEH001750}


Linking options:
  • http://mi.mathnet.ru/eng/izv1874
  • http://mi.mathnet.ru/eng/izv/v41/i4/p937

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. D. Gogoladze, “On strong summability almost everywhere”, Math. USSR-Sb., 63:1 (1989), 153–164  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. V. A. Rodin, “The tensor BMO-property of the sequence of partial sums of a multiple Fourier series”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 211–224  mathnet  crossref  mathscinet  zmath  isi
    4. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:213
    Full text:70
    References:35
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020