Randomised circular means of Fourier transforms of measures

Bennett, Jonathan; Vargas, Ana

doi:10.1090/S0002-9939-02-06696-0

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.

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