Skip to main content
SpringerLink
Log in

Convergence almost everywhere of certain singular integrals and multiple Fourier series

  • Published:
Arkiv för Matematik

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Calderón, A. P., andZygmund, A., On the existence of certain singular integrals.Acta Math. 88 (1952), 85–139.

    Article  MATH  MathSciNet  Google Scholar 

  2. ——, On singular integrals.Amer. J. Math. 78 (1956), 289–309.

    Article  MATH  MathSciNet  Google Scholar 

  3. ——, Algebras of certain singular operators.Amer. J. Math. 78 (1956), 310–320.

    Article  MATH  MathSciNet  Google Scholar 

  4. Carleson, L., On convergence and growth of partial sums of Fourier series.Acta Math. 116 (1966), 135–157.

    Article  MATH  MathSciNet  Google Scholar 

  5. Fefferman, C., On the convergence of multiple Fourier series. To appear.

  6. Fefferman, C., On the divergence of multiple Fourier series. To appear.

  7. Hunt, R. A., On the convergence of Fourier series. Orthogonal expansions and their continuous analogues.Proceedings of the Conference held at Southern Illinois University, Edwardsville, 1967. SIU Press, Carbondale, Illinois, 1968.

    Google Scholar 

  8. —, OnL(p, q) spaces.Enseignement Math. 12 (1966), 249–276.

    MATH  MathSciNet  Google Scholar 

  9. Kaczmarz, S., zur Theorie der Fourierschen Doppelreihen.Studia Math. 2 (1930), 91–96.

    Google Scholar 

  10. Shapiro, V. L., Fourier series in several variables.Bull. Amer. Math. Soc. 70 (1964), 48–93.

    Article  MATH  MathSciNet  Google Scholar 

  11. Sjölin, P., An inequality of Paley and convergence a.e. of Walsh — Fourier series.Ark. Mat. 7 (1968), 551–570.

    Article  Google Scholar 

  12. Stein, E. M., Localization and summability of multiple Fourier series.Acta Math. 100 (1958), 93–147.

    Article  MATH  MathSciNet  Google Scholar 

  13. — On certain exponential sums arising in multiple Fourier series.Ann. of Math. 73 (1961), 87–109.

    Article  MathSciNet  Google Scholar 

  14. Stein, E. M.,Intégrales singulières et fonctions différentiables de plusieurs variables. Publications Mathématiques d'Orsay, 1967.

  15. —, andWeiss, G., An extension of a theorem of Marcinkiewicz and some of its applications.J. Math. Mech. 8 (1959), 263–284.

    MATH  MathSciNet  Google Scholar 

  16. Tevzadze, N. R., On the convergence of the double Fourier series of quadratic summable functions (Russian).Svobŝĉ. Akad. Nauk Gruzin. SSR 58 (1970), 277–279.

    MATH  MathSciNet  Google Scholar 

  17. Zygmund, A., On certain lemmas of Marcinkiewicz and Carleson.J. Approximation Theory 2 (1969), 249–257.

    Article  MATH  MathSciNet  Google Scholar 

  18. Zygmund, A.,Trigonometric series, vol. I, 1959.

  19. Zygmund, A.,Trigonometric series, vol. II, 1959.

Download references

Author information

Authors and Affiliations

  1. Institut Mittag-Leffler, Auravägen 17, S-182 62, Djursholm, Sweden

    Per Sjölin

Authors
  1. Per Sjölin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sjölin, P. Convergence almost everywhere of certain singular integrals and multiple Fourier series. Ark. Mat. 9, 65–90 (1971). https://doi.org/10.1007/BF02383638

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02383638

Keywords

Search

Navigation