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

  • Lechao Xiao

    University of Pennsylvania, Philadelphia, USA

Abstract

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 , which may be of independent interest.

Cite this article

Lechao Xiao, Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities. Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 67–116

DOI 10.4171/RMI/928