|
Randomised circular means of Fourier transforms of measures
Author(s):
Jonathan
M.
Bennett;
Ana
Vargas
Journal:
Proc. Amer. Math. Soc.
131
(2003),
117-127.
MSC (2000):
Primary 42B10
Posted:
August 19, 2002
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We explore decay estimates for  circular means of the Fourier transform of a measure on  in terms of its  -dimensional energy. We find new upper bounds for the decay exponent. We also prove sharp estimates for a certain family of randomised versions of this problem.
References:
-
- 1.
- J. A. Barceló, Tesis Doctoral, Universidad Autónoma de Madrid, 1988.
- 2.
- J. A. Barceló, J. M. Bennett, A. Carbery, A bilinear extension estimate in two dimensions, preprint (2001).
- 3.
- J. A. Barceló, A. Ruiz, L. Vega, Weighted estimates for the Helmholtz equation and consequences, JFA Vol. 150 (1997), 2, 356-382. MR 99a:35033
- 4.
- J. Bourgain, Hausdorff dimension and distance sets, Israel J. Math. 87 (1994), 193-201. MR 95h:28008
- 5.
- A. Carbery, F. Soria, Pointwise Fourier inversion and localisation in
 , Journal of Fourier Analysis and Applications 3, special issue, 847-858 (1997). MR 99c:42018 - 6.
- A. Carbery, F. Soria, A. Vargas, preprint.
- 7.
- A. Córdoba, The Kakeya Maximal Functions and the Spherical Summation Multipliers, Am. J. Math. 99 (1977), 1-22. MR 56:6259
- 8.
- N. H. Katz, T. Tao, Some connections between Falconer's distance set conjecture, and sets of Furstenburg type, New York J. Math. 7 (2001), 149-187.
- 9.
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics 44. MR 96h:28006
- 10.
- P. Mattila, Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets, Mathematika 34 (1987), 207-228. MR 90a:42009
- 11.
- P. Sjölin, Estimates of spherical averages of Fourier transforms and dimensions of sets, Mathematika 40 (1993), 322-330. MR 95f:28007
- 12.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1944. MR 6:64a
- 13.
- T. H. Wolff, Decay of circular means of Fourier transforms of measures, Internat. Math. Res. Notices 10 (1999), 547-567. MR 2000k:42016
- 14.
- T. H. Wolff, Recent work connected with the Kakeya problem, Prospects in mathematics (Princeton, NJ, 1996), 129-162, Amer. Math. Soc., Providence, RI, 1999. MR 2000d:42010
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
42B10
Retrieve articles in all Journals with MSC
(2000):
42B10
Additional Information:
Jonathan
M.
Bennett
Affiliation:
Department of Mathematics, University Autonoma de Madrid, 28049 Madrid, Spain
Email:
jonathan.bennett@uam.es
Ana
Vargas
Affiliation:
Department of Mathematics, University Autonoma de Madrid, 28049 Madrid, Spain
Email:
ana.vargas@uam.es
DOI:
10.1090/S0002-9939-02-06696-0
PII:
S 0002-9939(02)06696-0
Keywords:
Fourier transforms,
circular means,
$\alpha$-energy
Received by editor(s):
April 27, 2001
Posted:
August 19, 2002
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org