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 to the full range . As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of in terms of the growth of the mapping.
Cite this article
Pekka Koskela, An inverse Sobolev lemma. Rev. Mat. Iberoam. 10 (1994), no. 1, pp. 123–141DOI 10.4171/RMI/147