Skip to main content
SpringerLink
Log in

Summability of differentiated multiple Fourier series by Bochner-Riesz means

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Literature cited

  1. A. Zygmund, Trigonometric Series, Cambridge Univ. Press.

  2. P. Pizzetti, “Sul significato geometrico del secondo parametro differenziale di una funzione sopra una superficie qualunque,” Rend. Delia Accad. Lincei, Ser. 5,18, 309–316 (1909).

    Google Scholar 

  3. V. L. Shapiro, “Circular summability C of double trigonometric series,” Trans. Am. Math. Soc.,76, No. 2, 223–233 (1954).

    Google Scholar 

  4. M. J. Kohn, “Spherical summability of differentiated multiple Fourier series,” Proc. Am. Math. Soc.,81, No. 4, 585–590 (1981).

    Google Scholar 

  5. M. J. Kohn, “On differentiation of multiple trigonometric series,” Illinois J. Math.,25, No. 2, 221–232 (1981).

    Google Scholar 

  6. G. H. Hardy, “The second theorem of consistency for summable series,” Proc. London Math. Soc.,15, 72–88 (1916).

    Google Scholar 

  7. T. H. Gronwall, “Über eine Summationsmethode und ihre Anwendung auf die Fouriersche Reihe,” J. Math.,147, 16–35 (1916).

    Google Scholar 

  8. A. Zygmund, “Sur un téorème de M. Gronwall,” Bull. Acad. Polonaise, 207–217 (1925).

  9. S. Bochner, “Summation of multiple Fourier series by spherical means,” Trans. Am. Math. Soc.,40, No. 2, 175–207 (1936).

    Google Scholar 

  10. S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  11. M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Tables, Dover (1964).

  12. H. Hochstadt, The Functions of Mathematical Physics, Interscience, New York (1971).

    Google Scholar 

  13. H. Lebesgue, “Recherches sur la convergence des series de Fourier,” Math. Ann.,61, 251–280 (1905).

    Google Scholar 

  14. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press (1971).

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. M. D'yachkov

Authors
  1. A. M. D'yachkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 36, No. 4, pp. 493–507, October, 1984.

Rights and permissions

Reprints and permissions

About this article

Cite this article

D'yachkov, A.M. Summability of differentiated multiple Fourier series by Bochner-Riesz means. Mathematical Notes of the Academy of Sciences of the USSR 36, 744–751 (1984). https://doi.org/10.1007/BF01156462

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01156462

Keywords

Search

Navigation