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Revista Matemática Iberoamericana

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Volume 10, Issue 1, 1994, pp. 123–141
DOI: 10.4171/RMI/147

Published online: 1994-04-30

An inverse Sobolev lemma

Pekka Koskela[1]

(1) University of Jyväskylä, Finland

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 $\mathbb R^n$ to the full range $0 < p < n$. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of $\mathbb R^n$ in terms of the growth of the mapping.

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Koskela Pekka: An inverse Sobolev lemma. Rev. Mat. Iberoam. 10 (1994), 123-141. doi: 10.4171/RMI/147