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Estimates of spherial averages of Fourier transforms and dimensions of sets

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Per Sjölin
Per Sjölin
Affiliation:
Matematiska institutionen, Uppsala Universitet, Box 480, S-75106 Uppsala, Sweden
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Extract

Let ℳ denote the class of all finite positive Borel measures μ in Rn with compact support. We define the Fourier transform of μεℳ by writing

and the α-energy of μ is given by

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 322 - 330
Copyright
Copyright © University College London 1993

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References

1.Mattila, P.. Spherical averages of Fourier transforms of measures with finite energy; dimension of intersections and distance sets. Mathematika, 34 (1987), 207–228.CrossRefGoogle Scholar