# Localisation and weighted inequalities for spherical Fourier means

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Article

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DOI: 10.1007/s11854-008-0004-x

- Cite this article as:
- Carbery, A., Soria, F. & Vargas, A. J Anal Math (2007) 103: 133. doi:10.1007/s11854-008-0004-x

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## Abstract

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.

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© The Hebrew University of Jerusalem 2007