Average decay of Fourier transforms and geometry of convex sets

• Autores: Luca Brandolini, Marco Rigoli, Giancarlo Travaglini
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 14, Nº 3, 1998, págs. 519-560
• Idioma: inglés
• Títulos paralelos:
  • Degradación media de las transformadas de Fourier y la geometría de conjuntos convexos
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• Resumen

  • Let B be a convex body in R2, with piecewise smooth boundary and let ^?B denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical Lp averages of ^?B and we relate our analysis to a problem in the geometry of convex sets. As an application we obtain sharp results on the average number of integer lattice points in large bodies randomly positioned in the plane.