Sublevel Set Estimates over Global Domains

2022/10/17 by Joonil Kim, Kim, Joonil
Computer Science · Mathematics · #42B25 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 42B20

paper · pdf · doi:10.48550/arxiv.2210.09029

openalex publication_date 2022/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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