Randomised circular means of Fourier transforms of measures

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF