Estimates for Fourier transforms of surface measures in R3 and PDE applications

• Michael Greenblatt ^[1]
  1. [1] University of Illinois at Chicago

     University of Illinois at Chicago

     City of Chicago, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 419-446
• Idioma: inglés
• DOI: 10.4171/RMI/890
• Texto completo no disponible (Saber más ...)
• Resumen

  • An explicit local two-dimensional resolution of singularities theorem and arguments based on the Van der Corput lemma are used to give new estimates for the decay rate of the Fourier transform of a locally defined smooth hypersurface measure in R3, as well as to provide new proofs of some known estimates. These are then used to give Lq bounds on solutions to certain PDE problems in terms of the Lp norms of their initial data for various values of p and q.