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arXiv · 1311.3725

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

Lechao Xiao
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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.

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Lechao Xiao. 2013-11-15. Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities. https://arxiv.org/abs/1311.3725

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