The classical Hardy space $H^2$ on the unit disc, and more generally Hilbert spaces of holomorphic functions, play an important role in operator theory and function theory. Weak product spaces generalize the notion of $H^1$ and were first studied using techniques from function theory and harmonic analysis.

I will talk about how weak product spaces carry the structure of an operator space and how this point of view makes it possible to characterize multipliers of weak products. This is joint work with Raphaël Clouâtre.