### Abstract

The point-wise product of a function of bounded mean oscillation with a function of the Hardy space H^{1} is not locally integrable in general. However, in view of the duality between H^{1} 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 H^{1} 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 - Jan 1 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

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## Cite this

^{1}.

*Annales de l'Institut Fourier*,

*57*(5), 1405-1439. https://doi.org/10.5802/aif.2299