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Factorization of some Hardy type spaces of holomorphic functions

We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space $\mathcal H^1$, the other one in its dual, belongs to a Hardy type space. Conversely, every holomorphic function in this space can be written as such a product. This generalizes previous characterization in the context of the unit disc.