Skip to main content
Log in

On criteria for the continuity of functions of bounded p-variation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature Cited

  1. N. Wiener, “The quadratic variation of a function and its Fourier coefficients.,” Massachusetts J. Math.,3, 72–94 (1924).

    Google Scholar 

  2. N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  3. S. M. Lozinskii, “On a theorem of N. Wiener,” Dokl. Akad. Nauk SSSR,49, No. 8, 562–565 (1945)

    Google Scholar 

  4. S. M. Nikol'skii, “The Fourier series of functions that have a derivative of bounded variation,” Izv. Akad. Nauk SSSR, Ser. Matem.13, No. 4, 513–532 (1949).

    Google Scholar 

  5. B. I. Golubov, “On continuous functions of bounded p-variation.,” Matem. Zametki,1, No. 3, 305–312 (1967).

    Google Scholar 

  6. B. I. Golubov, “On the p-variation of a function,” Matem. Zametki,5, No. 2, 195–204 (1969).

    Google Scholar 

  7. B. I. Golubov, “On functions of bounded p-variation,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 4, 837–858 (1968).

    Google Scholar 

  8. B. I. Golubov, “The Fourier integral and the continuity of functions of bounded p-variation,” Izv. Vyssh. Ucheb. Zaved. Matematika,11, (78), 83–92 (1968).

    Google Scholar 

  9. B. I. Golubov, “On the analogues of the theorems of Wiener and of Lozinskii for functions of several variables,” Trudy Tbilissk. Matem. Inst.,38, 31–43 (1970).

    Google Scholar 

  10. W. W. Rogosinski, “Über die Abschnitte trigonometrischer Reihe,” Math. Ann.,95, 110–134 (1925).

    Google Scholar 

  11. S. Sidon, “Über die Fouriercoeffizienten einer stetigen Funktion von beschrankter Schwankung,” Acta. Sci. Math.,2, 43–46 (1924).

    Google Scholar 

  12. L. Fejer, “Über die Bestimmung des Sprunges einer Funktion aus ihre Fourierreihe,” J. fur Math.,142, 165–188 (1913).

    Google Scholar 

  13. P. Szillag, “On the Fourier coefficients of a function of bounded variation [in Hungarian],” Math. es Phys. Lapok,27, 301–308 (1918).

    Google Scholar 

  14. A. Zygmund, Trigonometric Series, Vol. I [Russian translation], Mir, Moscow (1965).

    Google Scholar 

  15. V. A. Matveev, “On the theorems of Wiener and of Lozinskii,” Investigations on Contemporary Problems in the Constructive Theory of Functions [in Russian], Baku (1965), pp. 460–468.

  16. L. C. Young, “An inequality of the Hölder type connected with Stieltjes integration,” Acta Math.,67, 251–282 (1936).

    Google Scholar 

  17. A. P. Terekhin, “The approximation of functions of bounded p-variation,” Izv. Vyssh. Ucheb. Zaved. Matematika,2 (45), 171–187 (1965).

    Google Scholar 

  18. G. H. Hardy, “Weierstrass's nondifferentiable function.,” Trans. Amer. Math. Soc.,17, 301–325 (1916).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 13, No. 5, pp. 1002–1015, September–October, 1972.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Golubov, B.I. On criteria for the continuity of functions of bounded p-variation. Sib Math J 13, 693–702 (1972). https://doi.org/10.1007/BF00968383

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00968383

Navigation