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On solutions of the Beltrami equation. (English) Zbl 0921.30015
The result of G. David [Ann. Acad., Sci. Fenn., Ser. A I, Math. 13, 25-70 (1988; Zbl 0619.30024)] concerning plane BMO – quasiconformal mappings has attracted a lot of research. In general \(\| \mu_f\|_\infty=1\) for such a mapping \(f\). The authors introduce two integral conditions for \(\mu_f\) and prove the existence and uniqueness result for \(f\) under these conditions; these provide an extension of the result of G. David. The proofs are based on the approximation method for \(f\) where the cut-off approach for \(\mu_f\) is used. This was already employed by G. David but the estimates are more elaborate in this case.

MSC:
30C62 Quasiconformal mappings in the complex plane
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