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A note on the distance set problem in the plane
Author(s):
Themis
Mitsis
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1669-1672.
MSC (2000):
Primary 28A12, 28A78
Posted:
October 12, 2001
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Abstract:
We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.
References:
- 1.
- Carleson, L. Selected problems on exceptional sets, Van Nostrand Math. Studies 13, Van Nostrand, Princeton, N.J., 1967. MR 37:1576
- 2.
- Falconer, K.J. On the Hausdorff dimension of distance sets, Mathematika 32 (1985), 206-212. MR 87j:28008
- 3.
- Mattila, P. Spherical averages of Fourier transforms of measures with finite energy; dimension of intersections and distance sets, Mathematika 34 (1987), 207-228. MR 90a:42009
- 4.
- Wolff, T. Decay of circular means of Fourier transforms of measures, Internat. Math. Res. Notices (1999), 547-567. MR 2000k:42016
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Additional Information:
Themis
Mitsis
Affiliation:
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
Address at time of publication:
Nestou 6, Athens 14342, Greece
Email:
mitsis@math.jyu.fi, tmitsis@yahoo.com
DOI:
10.1090/S0002-9939-01-06375-4
PII:
S 0002-9939(01)06375-4
Received by editor(s):
November 21, 2000
Posted:
October 12, 2001
Additional Notes:
This research has been supported by a Marie Curie Fellowship of the European Community programme ``Improving human potential and the socio-economic knowledge base" under contract number HPMFCT-2000-00442.
Communicated by:
David Preiss
Copyright of article:
Copyright
2001,
American Mathematical Society
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