On zero varieties of holomorphic functions in Hardy spaces ✩

In contrast to the famous Henkin–Skoda theorem concerning the zero varieties of holomorphic functions in the Nevanlinna class on the open unit ball Bn in Cn, n 2, it is proved in this article that for any nonnegative, increasing, convex function ϕ(t) defined on R, there exists g ∈ O(Bn) satisfying S ϕ(Ng(ζ, 1)) dσ (ζ ) < ∞ such that there is no f ∈ Hp(Bn), 0 < p < ∞, with Z(f ) = Z(g). Here Ng(ζ, 1) denotes the integrated zero counting function associated with the slice function gζ . This means that the zero sets of holomorphic functions belonging to the Hardy spaces Hp(Bn), 0