A study of Jacobians in Hardy-Orlicz spaces

Tadeusz Iwaniec, Anna Verde

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We study the Jacobian determinants J = det(∂fi/∂xj) of mappings f : Ω ⊂ ℝn → ℝn in a Sobolev-Orlicz space W1,Φ(Ω, ℝn). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy-Orlicz spaces HP(Ω). Other nonlinear quantities involving the Jacobian, such as J log|J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.

Original languageEnglish (US)
Pages (from-to)539-570
Number of pages32
JournalRoyal Society of Edinburgh - Proceedings A
Issue number3
StatePublished - 1999

ASJC Scopus subject areas

  • General Mathematics


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