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A note on the distance set problem in the plane


Author: Themis Mitsis
Journal: Proc. Amer. Math. Soc. 130 (2002), 1669-1672
MSC (2000): Primary 28A12, 28A78
DOI: https://doi.org/10.1090/S0002-9939-01-06375-4
Published electronically: October 12, 2001
MathSciNet review: 1887013
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Abstract | References | Similar Articles | Additional Information

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

  • 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: https://doi.org/10.1090/S0002-9939-01-06375-4
Received by editor(s): November 21, 2000
Published electronically: 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
Article copyright: © Copyright 2001 American Mathematical Society

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