Revista Matemática Iberoamericana


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Volume 33, Issue 1, 2017, pp. 67–116
DOI: 10.4171/RMI/928

Published online: 2017-02-22

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

Lechao Xiao[1]

(1) University of Pennsylvania, Philadelphia, USA

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 $\mathbb R^2$, which may be of independent interest.

Keywords: Multilinear operators, oscillatory integrals, resolution of singularities, Newton polyhedra

Xiao Lechao: Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities. Rev. Mat. Iberoamericana 33 (2017), 67-116. doi: 10.4171/RMI/928