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On the product of functions in H 1 and BMO. Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister. The space BMO:. The Hardy space H 1. 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. - PowerPoint PPT Presentation
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On the product of functions in H1 and BMO
Aline Bonami,
Tadeusz Iwaniec,
Peter Jones,
Michel Zinsmeister
The space BMO:
The Hardy space H1
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
Two (equivalent) ways to define the duality
What can be said about this distribution?
The answer involves the notion of Orlicz space
This theorem has a converse in the case of the disc, in the holomorphic setting:
Idea of proofs:
Proof of the theorem about holomorphic Hardy spaces