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

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 .