Randomised circular means of Fourier transforms of measures
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- by Jonathan M. Bennett and Ana Vargas PDF
- Proc. Amer. Math. Soc. 131 (2003), 117-127 Request permission
Abstract:
We explore decay estimates for $L^1$ circular means of the Fourier transform of a measure on $\mathbb {R}^2$ in terms of its $\alpha$–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
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Additional Information
- Jonathan M. Bennett
- Affiliation: Department of Mathematics, University Autonoma de Madrid, 28049 Madrid, Spain
- MR Author ID: 625531
- Email: jonathan.bennett@uam.es
- Ana Vargas
- Affiliation: Department of Mathematics, University Autonoma de Madrid, 28049 Madrid, Spain
- Email: ana.vargas@uam.es
- Received by editor(s): April 27, 2001
- Published electronically: August 19, 2002
- Communicated by: Andreas Seeger
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 117-127
- MSC (2000): Primary 42B10
- DOI: https://doi.org/10.1090/S0002-9939-02-06696-0
- MathSciNet review: 1929031