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Randomised circular means of Fourier transforms of measures


Authors: Jonathan M. Bennett and Ana Vargas
Journal: Proc. Amer. Math. Soc. 131 (2003), 117-127
MSC (2000): Primary 42B10
Published electronically: August 19, 2002
MathSciNet review: 1929031
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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.


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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: https://doi.org/10.1090/S0002-9939-02-06696-0
Keywords: Fourier transforms, circular means, $\alpha$-energy
Received by editor(s): April 27, 2001
Published electronically: August 19, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society