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arXiv · 0707.2557

Uniform estimates for cubic oscillatory integrals

Philip T. Gressman
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Abstract

This paper establishes the optimal decay rate for scalar oscillatory integrals in $n$ variables which satisfy a nondegeneracy condition on the third derivatives. The estimates proved are stable under small linear perturbations, as encountered when computing the Fourier transform of surface-carried measures. The main idea of the proof is to construct a nonisotropic family of balls which locally capture the scales and directions in which cancellation occurs.

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Philip T. Gressman. 2007-07-19. Uniform estimates for cubic oscillatory integrals. https://arxiv.org/abs/0707.2557

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