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Sharp estimates in some inequalities of Zygmund type for Riesz transforms

Authors: Jorge Aarão and Michael D. O’Neill
Journal: Proc. Amer. Math. Soc. 140 (2012), 4227-4233
MSC (2010): Primary 26D07, 42B20, 60H30
Published electronically: July 18, 2012
Previous version: Original version posted April 13, 2012
Current version: Corrects first author's affiliation and mailing address
MathSciNet review: 2957213
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Abstract | References | Similar Articles | Additional Information

Abstract: Sharp constant versions of two endpoint inequalities for Riesz transforms are derived using probabilistic methods.

References [Enhancements On Off] (What's this?)

  • 1. R. Bañuelos and G. Wang,
    Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms.
    Duke Math. J., 80 (3):575-600, 1995. MR 1370109 (96k:60108)
  • 2. R. F. Bass,
    Probabilistic Techniques in Analysis,
    Probability and its Applications (New York),
    Springer-Verlag, New York, 1995. MR 1329542 (96e:60001)
  • 3. D. Burkholder,
    A sharp inequality for martingale transforms.
    Ann. Probab., 7:858-863, 1979. MR 542135 (80j:60067)
  • 4. A. Calderon and A. Zygmund,
    On the existence of certain singular integrals.
    Acta Math., 88:85-139, 1952. MR 0052553 (14:637f)
  • 5. T. Gamelin,
    Uniform Algebras and Jensen Measures.
    London Math. Society Lecture Notes Series, 32,
    Cambridge University Press, London and New York, 1978. MR 521440 (81a:46058)
  • 6. R. Gundy and N. Varopoulos,
    Les transformations de Riesz et les intégrales stochastiques. (French),
    C.R. Acad. Sci. Paris Sér. A-B, 289 (1):A13-A16, 1979. MR 545671 (82e:60089)
  • 7. S. Pichorides,
    On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov.
    Studia Math., 44:165-179, 1972. MR 0312140 (47:702)
  • 8. E. Stein,
    Singular Integrals and Differentiability Properties of Functions.
    Princeton Mathematical Series, No. 30,
    Princeton University Press, New Jersey, 1970. MR 0290095 (44:7280)
  • 9. A. Zygmund,
    Sur les fonctions conjugées.
    Fund. Math., 13:284-303, 1929.
  • 10. A. Zygmund,
    Trigonometric Series.
    Paperback edition, volumes I and II combined.
    Cambridge University Press, Cambridge, 1988. MR 933759 (89c:42001)

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Additional Information

Jorge Aarão
Affiliation: School of Mathematics and Statistics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, 5070 SA, Australia

Michael D. O’Neill
Affiliation: Department of Mathematics, Claremont McKenna College, Claremont, California 91711

Received by editor(s): May 26, 2011
Published electronically: July 18, 2012
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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