JournalsrmiVol. 10, No. 1pp. 123–141

An inverse Sobolev lemma

  • Pekka Koskela

    University of Jyväskylä, Finland
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Abstract

We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of Rn\mathbb R^n to the full range 0<p<n0 < p < n. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of Rn\mathbb R^n in terms of the growth of the mapping.

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Pekka Koskela, An inverse Sobolev lemma. Rev. Mat. Iberoam. 10 (1994), no. 1, pp. 123–141

DOI 10.4171/RMI/147