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

Abstract

We obtain sharp estimates for certain trilinear oscillatory integrals. In particular, we extend Phong and Stein's seminal result to a trilinear setting. This result partially answers a question raised by Christ, Li, Tao and Thiele concerning the sharp estimates for certain multilinear oscillatory integrals. The method in this paper relies on a self-contained algorithm of resolution of singularities in ${\mathbb{R}}^2$, which may be of independent interest.

46 pages, 8 figures; Referees' comments incorporated; to appear in Revista Matemática Iberoamericana

References in corpus (1)

• Multilinear Oscillatory Integrals Via Reduction of Dimension

Cited by in corpus (3)

• Higher decay inequalities for multilinear oscillatory integrals
• Maximal Decay Inequalities for Trilinear oscillatory integrals of convolution type
• Endpoint estimates for one-dimensional oscillatory integral operator