Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

   
 

 

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
Full-text PDF

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. Rodrigo Bañuelos and Gang Wang, Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. J. 80 (1995), no. 3, 575–600. MR 1370109, 10.1215/S0012-7094-95-08020-X
  • 2. Richard F. Bass, Probabilistic techniques in analysis, Probability and its Applications (New York), Springer-Verlag, New York, 1995. MR 1329542
  • 3. D. L. Burkholder, A sharp inequality for martingale transforms, Ann. Probab. 7 (1979), no. 5, 858–863. MR 542135
  • 4. A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 0052553
  • 5. T. W. Gamelin, Uniform algebras and Jensen measures, London Mathematical Society Lecture Note Series, vol. 32, Cambridge University Press, Cambridge-New York, 1978. MR 521440
  • 6. Richard F. Gundy and Nicolas Th. Varopoulos, Les transformations de Riesz et les intégrales stochastiques, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), no. 1, A13–A16 (French, with English summary). MR 545671
  • 7. S. K. Pichorides, On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), 165–179. (errata insert). Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, II. MR 0312140
  • 8. Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
  • 9. A. Zygmund,
    Sur les fonctions conjugées.
    Fund. Math., 13:284-303, 1929.
  • 10. A. Zygmund, Trigonometric series. Vol. I, II, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988. Reprint of the 1979 edition. MR 933759

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 26D07, 42B20, 60H30

Retrieve articles in all journals with MSC (2010): 26D07, 42B20, 60H30


Additional Information

Jorge Aarão
Affiliation: School of Mathematics and Statistics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, 5070 SA, Australia
Email: Jorge.Aarao@unisa.edu.au

Michael D. O’Neill
Affiliation: Department of Mathematics, Claremont McKenna College, Claremont, California 91711
Email: moneill@cmc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11353-X
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.