论文标题
对全球域的级别设定估算
Sublevel Set Estimates over Global Domains
论文作者
论文摘要
自从Varchenko的开创性论文以来，通过与相$ P $相关的牛顿Polyhedra阐明了振荡积分和相关问题的渐近学。这些积分的支持集中在足够小的社区上。 本文的目的是调查子级和振荡积分的估计值，其支持是全球域$ d $。 $ d $的基本型号是$ \ mathbb {r}^d $。为此，我们定义了与$（P，D）$相关的Newton Polyhedra，并在全球域中$ d $的Varchenko定理建立类似物，在$ p $的非分类条件下。
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 $P$.
