Localisation and weighted inequalities for spherical Fourier means
- 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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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 L2-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.