Revista Matemática Iberoamericana
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Published online: 2017-02-22
Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularitiesLechao Xiao (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