Journal d'Analyse Mathématique

, Volume 103, Issue 1, pp 133–156

Localisation and weighted inequalities for spherical Fourier means

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.

Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  1. 1.School of Mathematics and Maxwell Institute for Mathematical SciencesUniversity of EdinburghEdinburghScotland
  2. 2.Departamento de Matemáticas, Facultad de CienciasUniversidad Autonóma de MadridMadridSpain