Abstract
The point-wise product of a function of bounded mean oscillation with a function of the Hardy space H1 is not locally integrable in general. However, in view of the duality between H1 and BMO, we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with holomorphic functions in the unit disc, the converse is also valid: every holomorphic of the corresponding Hardy-Orlicz space can be written as a product of a function in the holomorphic Hardy space H1 and a holomorphic function with boundary values of bounded mean oscillation.
Original language | English (US) |
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Pages (from-to) | 1405-1439 |
Number of pages | 35 |
Journal | Annales de l'Institut Fourier |
Volume | 57 |
Issue number | 5 |
DOIs | |
State | Published - 2007 |
Keywords
- Bounded mean oscillation
- Div-curl lemma
- Factorization in hardy spaces
- Hardy spaces
- Hardy-Orlicz spaces
- Jacobian equation
- Jacobian lemma
- Weak jacobian
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology