Journal d'Analyse Mathématique

, Volume 103, Issue 1, pp 133–156

Localisation and weighted inequalities for spherical Fourier means

Authors

    • School of Mathematics and Maxwell Institute for Mathematical SciencesUniversity of Edinburgh
  • Fernando Soria
    • Departamento de Matemáticas, Facultad de CienciasUniversidad Autonóma de Madrid
  • Ana Vargas
    • Departamento de Matemáticas, Facultad de CienciasUniversidad Autonóma de Madrid
Article

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

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 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.

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© The Hebrew University of Jerusalem 2007