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On the product of functions in H 1 and BMO

Explore the relationship between BMO and H1 functions using Orlicz space notions in the context of distribution duality.

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On the product of functions in H 1 and BMO

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  1. On the product of functions in H1 and BMO Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister

  2. The space BMO:

  3. The Hardy space H1

  4. Fefferman-Stein: BMO is the dual of H1 But this duality is not like Lp-Lq i.e. bh need not be integrable if b is in BMO and h is in H1

  5. Two (equivalent) ways to define the duality

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

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

  8. Idea of proofs:

  9. Proof of the theorem about holomorphic Hardy spaces

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