Skip to main content
SpringerLink
Log in

Some properties of fractional integrals. I.

  • Published:
Mathematische Zeitschrift 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

Memoirs and books referred to

  1. Bernstein, S.: Sur la convergence absolue des séries trigonométriques, Comptes rendus, 8 June 1914.

  2. Hardy, G. H.: Some properties of integrals of fractional order, Messenger of Mathematics47 (1918), p. 145–150.

    Google Scholar 

  3. —: Weierstrass's non-differentiable function, Trans. Amer. Math. Soc.17 (1916), p. 301–325.

    Google Scholar 

  4. Hardy, G. H., and Littlewood, J. E.: Some properties of fractional integrals, Proc. London Math. Soc. (2),24 (1925), p. xxxvii-xli (Records for 12 March 1925).

    Google Scholar 

  5. ——: On Parseval's Theorem, Proc. London Math. Soc. (2),26 (1927), p. 287–294.

    Google Scholar 

  6. Hardy, G. H., Littlewood, J. E., Pólya, G.: The maximum of a certain bilinear form, Proc. London Math. Soc. (2),25 (1926), p. 265–282.

    Google Scholar 

  7. Jordan, C.: Cours d'analyse, ed. 2,3 (1896), p. 58–59.

    Google Scholar 

  8. Liouville, J.: Sur le calcul des différentielles à indices quelconques, Journal de l'École Polytechnique13 (1832), p. 1–69.

    Google Scholar 

  9. Pollard, S.: On Parseval's Theorem, Proc. London Math. Soc. (2),25 (1926), p. 237–246 (240).

    Google Scholar 

  10. Riemann, B.: Versuch einer allgemeinen Auffassung der Integration und Differentiation, Werke, p. 331–344.

  11. Riesz, F.: Untersuchungen über Systeme integrierbarer Funktionen, Math. Annalen69 (1910), p. 449–497.

    Google Scholar 

  12. Riesz, M.: Les fonctions conjuguées et les séries de Fourier, Comptes rendus, 28 April 1924.

  13. —: Sur les fonctions conjuguées, Math. Zeitschr.27 (1927), p. 218–244.

    Google Scholar 

  14. Schlesinger, L., und Plessner, A., Lebesguesche Integrale und Fouriersche Reihen, Berlin 1926.

  15. Szász, O.: Über den Konvergenzexponenten der Fourierschen Reihen gewisser Funktionenklassen, Münchener Sitzungsberichte (1922), p. 135–150.

  16. Titchmarsh, E. C.: Reciprocal formulae for series and integrals, Math. Zeitschr.25 (1926), p. 321–347.

    Google Scholar 

  17. —: A note on Fourier transforms, Journal London Math. Soc.2 (1927), p. 148–150.

    Google Scholar 

  18. Weyl, H.: Bemerkungen zum Begriff des Differentialquotienten gebrochener Ordnung, Vierteljahrsschrift d. naturf. Ges. in Zürich,62 (1917), p. 296–302.

    Google Scholar 

  19. Zygmund, A: Sur la sommabilité des séries de Fourier des fonctions vérifiant la condition de Lipschitz, Bulletin de l'Acad. de Cracovie (1925), p. 1–9.

Download references

Author information

Authors and Affiliations

  1. Oxford

    G. H. Hardy

  2. Cambridge

    J. E. Littlewood

Authors
  1. G. H. Hardy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. E. Littlewood
    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

Hardy, G.H., Littlewood, J.E. Some properties of fractional integrals. I.. Math Z 27, 565–606 (1928). https://doi.org/10.1007/BF01171116

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01171116

Search

Navigation