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

DOI:
https://doi.org/10.1090/S0002-9939-02-06696-0

Published electronically:
August 19, 2002

MathSciNet review:
1929031

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Abstract | References | Similar Articles | Additional Information

Abstract: We explore decay estimates for circular means of the Fourier transform of a measure on in terms of its -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