Skip to main content
SpringerLink
Log in

A probabilistic approach to the boundedness of singular integral operators

  • Conference paper
  • First Online:
Séminaire de Probabilités XXIV 1988/89

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1426))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bañuelos, R.: Martingale transforms and related singular integrals. Trans. Amer. Math. Soc. 293, 547–563 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bennett, A.: Probabilistic square functions and a priori estimates. Trans. Amer. Math. Soc. 291, 159–166 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  3. Bouleau, N., Lamberton, D.: Théorie de Littlewood-Paley et processus stables. C.R. Acad. Sc. Paris 299, 931–934 (1984).

    MathSciNet  MATH  Google Scholar 

  4. Bourgain, J.: Vector-valued singular integrals and the H 1-BMO duality. In: Chao, J.A, Woyczynski, W.A. (eds.) Probability Theory and Harmonic Analysis (pp. 1–19) New York: Marcel Dekker 1986.

    Google Scholar 

  5. Burkholder, D.L.: A geometric condition that implies that existence of certain singular integrals of Banach-space-valued functions. In: Becker, W., Calderón, A.P., Fefferman, R., Jones, P.W. (eds.) Conference on Harmonic Analysis in Honor of Antoni Zygmund (vol. 1, pp. 270–286). Belmont CA: Wadsworth 1983.

    Google Scholar 

  6. David, G., Journé, J.-L.: A boundedness criterion for generalized Calderón-Zygmund operators. Ann. Math. 120, 371–397 (1984).

    Article  MATH  Google Scholar 

  7. Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel: théorie des martingales. Paris: Hermann 1980.

    MATH  Google Scholar 

  8. Durrett, R.: Brownian motion and martingales in analysis, Belmont CA: Wadsworth 1984.

    MATH  Google Scholar 

  9. Erdelyi, A.: Tables of integral transforms, Vol. 1. New York: McGraw-Hill 1954.

    MATH  Google Scholar 

  10. Getoor, R.K., Sharpe, M.J.: Excursions of Brownian motion and Bessel processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 47, 83–106 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  11. Gundy, R.F., Silverstein, M.: On a probabilistic interpretation for the Riesz transforms. In: Fukushima, M. (ed.), Functional analysis in Markov processes (pp. 199–203). New York: Springer 1982.

    Chapter  Google Scholar 

  12. Gundy, R.F., Varopoulos, N.: Les transformations de Riesz et les integrales stochastiques. C.R. Acad. Sci. Paris 289, 13–16 (1979).

    MathSciNet  MATH  Google Scholar 

  13. Marias, M.: Littlewood-Paley-Stein theory and Bessel diffusions. Bull. Sci. Math. 111, 313–331 (1987).

    MathSciNet  MATH  Google Scholar 

  14. McConnell, T.R.: On Fourier multiplier transformations of Banach-valued functions. Trans. Amer. Math. Soc. 285, 739–757 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  15. Meyer, P.-A.: Démonstration probabiliste de certaines inégalités de Littlewood-Paley. In: Meyer, P.-A. (ed.) Séminaire de Probabilités X (pp. 125–183). New York: Springer 1976.

    Google Scholar 

  16. Rubio de Francia, J.L.: Factorization theory and A p weights. Am. J. Math. 106, 533–547 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  17. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton: Princeton Univ. Press 1970.

    MATH  Google Scholar 

  18. Torchinsky, A.: Real variable methods in harmonic analysis. New York: Academic Press 1986.

    MATH  Google Scholar 

  19. Varopoulos, N.Th.: Aspects of probabilistic Littlewood-Paley theory. J. Funct. Anal. 38, 25–60 (1980).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    Richard F. Bass

Authors
  1. Richard F. Bass
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jacques Azéma Marc Yor Paul André Meyer

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Bass, R.F. (1990). A probabilistic approach to the boundedness of singular integral operators. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIV 1988/89. Lecture Notes in Mathematics, vol 1426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083754

Download citation

  • DOI: https://doi.org/10.1007/BFb0083754

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52694-0

  • Online ISBN: 978-3-540-47098-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation