Original article

Mathematische Annalen

, Volume 324, Issue 2, pp 341-358

First online:

\({\cal H}^1\)-estimates of Jacobians by subdeterminants

  • Tadeusz IwaniecAffiliated withDepartment of Mathematics, Syracuse University, Syracuse, NY 13244, USA (e-mail: tiwaniec@mailbox.syr.edu)
  • , Jani OnninenAffiliated withDepartment of Mathematics, University of Jyväskylä , P.O. Box 35, Fin-40351 Jyväskylä, Finland (e-mail: jaonnine@math.jyu.fi)

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Let \(f:\Omega \rightarrow{\Bbb R}^n\) be a mapping in the Sobolev space \(W^{1,n-1}_{loc}(\Omega,{\Bbb R}^n), n\geq 2\). We assume that the cofactors of the differential matrix Df(x) belong to \(L^\frac{n}{n-1}(\Omega)\). Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space \({\cal H}^1(\Omega)\).

Mathematics Subject Classification (2000): 42B25, 26B10