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

TL;DR

This paper establishes a condition characterizing when a divisor in a bounded convex domain of finite type in C^n is the zero set of a Hardy space H^p function, extending previous results to more general convex domains.

Contribution

It generalizes Varopoulos' 1980 result by providing a new criterion for zero sets of H^p functions in convex domains of finite type in complex n-space.

Findings

Provides a necessary and sufficient condition for zero sets in convex finite type domains.

Extends classical results from strictly convex to more general convex domains.

Enhances understanding of zero sets in several complex variables.

Abstract

We give a condition under which a divisor X in a bounded convex domain of finite type D in C^n 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 C^n .