On the product of functions in BMO and H1

Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister

Research output: Contribution to journalArticle

65 Scopus citations

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 languageEnglish (US)
Pages (from-to)1405-1439
Number of pages35
JournalAnnales de l'Institut Fourier
Volume57
Issue number5
DOIs
StatePublished - 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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