Algorithms for subelliptic multipliers in ℂ²

2020/02/28 by Martino Fassina, Fassina, Martino
Mathematics · #32T25 #32W05 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2003.00128

openalex publication_date 2020/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give examples of pseudoconvex domains of finite type in ℂ² where the Kohn algorithm for subelliptic estimates fails to yield an effective lower bound for the order of subellipticity in terms of the type. We show how to modify the algorithm to obtain an effective procedure to prove subellipticity on domains of finite type in ℂ² with real analytic boundary satisfying a condition slightly stronger than pseudoconvexity. We close with a generalization to higher dimensions.

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