Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities

• Lechao Xiao ^[1]
  1. [1] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 1, 2017, págs. 67-116
• Idioma: inglés
• DOI: 10.4171/RMI/928
• Texto completo no disponible (Saber más ...)
• Resumen

  • We obtain sharp estimates for certain trilinear oscillatory integrals, extending Phong and Stein’s seminal result to a trilinear setting. This result partially answers a question raised by Christ, Li, Tao and Thiele, concerning sharp estimates for certain multilinear oscillatory integrals. The method in this paper relies on a self-contained algorithm of resolution of singularities in R2, which may be of independent interest.