, Volume 103, Issue 1, pp 133-156

Localisation and weighted inequalities for spherical Fourier means

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In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L 2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.

The research of this paper has been partially supported by the EU Comission via the network HARP, and by MEC Grant MTM2004-00678.
The first author was partially supported by a Leverhulme Study Abroad Fellowship.