Compact families ofBMO-quasiconformal mappings I

Families of quasiconformal homeomorphisms of bounded mean oscillation (BMO-qc) are studied from the point of view of compacity (normality + closedness). Using Tukia's convergence theorems and David's existence and factorization theorem, a normality criterion for families ofBMO-qc homeomorphisms and a compacity criterion for families transforming a given compact subsetM 1 in a compact subsetM 2 are established.