Localisation and weighted inequalities for spherical Fourier means

Anthony Carbery, Fernando Soria, Ana Vargas

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Abstract / Description of output

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.

Original languageEnglish
Pages (from-to)133-156
Number of pages24
JournalJournal d'Analyse Mathématique
Publication statusPublished - Dec 2007

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