Mathematische Annalen

, Volume 324, Issue 2, pp 341–358

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

  • Tadeusz Iwaniec
  • Jani Onninen
Original article

DOI: 10.1007/s00208-002-0341-5

Cite this article as:
Iwaniec, T. & Onninen, J. Math Ann (2002) 324: 341. doi:10.1007/s00208-002-0341-5


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

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Tadeusz Iwaniec
    • 1
  • Jani Onninen
    • 2
  1. 1.Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA (e-mail: US
  2. 2.Department of Mathematics, University of Jyväskylä , P.O. Box 35, Fin-40351 Jyväskylä, Finland (e-mail: FI