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arXiv · 2210.09029

Sublevel Set Estimates over Global Domains

Joonil Kim
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Abstract

Since Varchenko's seminal paper, the asymptotics of oscillatory integrals and related problems have been elucidated through the Newton polyhedra associated with the phase $P$. The supports of those integrals are concentrated on sufficiently small neighborhoods. The aim of this paper is to investigate the estimates of sub-level-sets and oscillatory integrals whose supports are global domains $D$. A basic model of $D$ is $ \mathbb{R}^d$. For this purpose, we define the Newton polyhedra associated with $(P,D)$ and establish analogues of Varchenko's theorem in global domains $D$, under non-degeneracy conditions of $P$.

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Joonil Kim. 2022-10-17. Sublevel Set Estimates over Global Domains. https://arxiv.org/abs/2210.09029

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