Examples of measures with slow decay of the spherical means of the Fourier transform

Ponce Vanegas, Felipe

doi:10.1090/proc/13999

Examples of measures with slow decay of the spherical means of the Fourier transform
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by Felipe Ponce Vanegas PDF

Proc. Amer. Math. Soc. 146 (2018), 2617-2621 Request permission

Abstract:

Many authors have studied the rate of average decay of the Fourier transform of measures because of its relationship with the Falconer’s conjecture. Although examples have been given showing that the spherical average of the Fourier transform cannot decay always too fast, they usually do not exhibit a single measure decaying sufficiently slow on the whole space. We recover known results using instead single measures.

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