1. On the product of functions in H 1 and BMO Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister

2. The space BMO:

3. The Hardy space H 1

4. Fefferman-Stein: BMO is the dual of H 1 But this duality is not like L p -L q i.e. bh need not be integrable if b is in BMO and h is in H 1

5. Two (equivalent) ways to define the duality

9. What can be said about this distribution? The answer involves the notion of Orlicz space

11. This theorem has a converse in the case of the disc, in the holomorphic setting:

14. Idea of proofs:

17. Proof of the theorem about holomorphic Hardy spaces