Zero Sets of H^p Functions in Convex Domains of Finite Type

2016/02/11 by William Alexandre, Alexandre, William
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1602.03848

openalex publication_date 2016/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a condition under which a divisor X in a bounded convex domain of finite type D in Cⁿ is the zero set of a function in a Hardy space H^p(D) for some p \textgreater 0. This generalizes Varopoulos' result [Zero sets of H^p functions in several complex variables, Pac. J. Math. (1980)] on zero sets of H^p-functions in strictly convex domains of Cⁿ .

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