RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ural Math. J.:
Year:
Volume:
Issue:
Page:
Find






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


Ural Math. J., 2017, Volume 3, Issue 2, Pages 14–21 (Mi umj38)  

On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series

Nikolai Yu. Antonov

Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: We consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the $\lambda $-convergence for $\lambda >1$. The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class $ L (\ln ^ + L) ^ d \ln ^ + \ln ^ + \ln ^ + L ([0,2 \pi)^d ) $ has been generalized to the case of the $ \Lambda $-convergence for some sequences $\Lambda$.

Keywords: Trigonometric Fourier series, Rectangular partial sums, Convergence almost everywhere.

Funding Agency Grant Number
Russian Science Foundation 14-11-00702
This work was supported by the Russian Science Foundation (project no. 14-11-00702).


DOI: https://doi.org/10.15826/umj.2017.2.003

Full text: PDF file (113 kB)
Full text: https:/.../99
References: PDF file   HTML file

Language:

Citation: Nikolai Yu. Antonov, “On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series”, Ural Math. J., 3:2 (2017), 14–21

Citation in format AMSBIB
\Bibitem{Ant17}
\by Nikolai~Yu.~Antonov
\paper On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 2
\pages 14--21
\mathnet{http://mi.mathnet.ru/umj38}
\crossref{https://doi.org/10.15826/umj.2017.2.003}


Linking options:
  • http://mi.mathnet.ru/eng/umj38
  • http://mi.mathnet.ru/eng/umj/v3/i2/p14

    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
  • Ural Mathematical Journal
    Number of views:
    This page:125
    Full text:46
    References:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019