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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
Posted:
July 18, 2012
Previous version:
Original version posted April 13, 2012
Current version:
Corrects first author's affiliation and mailing address
Full-text PDF
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Additional Information
Abstract: Sharp constant versions of two endpoint inequalities for Riesz transforms are derived using probabilistic methods.
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(81a:46058)
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A-B 289 (1979), no. 1, A13–A16 (French, with
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(82e:60089)
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K. Pichorides, On the best values of the constants in the theorems
of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44
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(89c:42001)
- 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)
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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
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
PII:
S 0002-9939(2012)11353-X
Received by editor(s):
May 26, 2011
Posted:
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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