Change of variables for A_\infty weights by means of quasiconformal mappings

Let f: Rn→Rn be a quasiconformal mapping whose Jacobian is denoted by Jf and let A∞ be the Muckenhoupt class of weights ω satisfying for every ball B ⊂ Rn and for some positive constant A ≥ 1 independent of B. We consider two characteristic constants ~ à _{(ω) and G̃1 (ω) which are simultaneously finite for every ω σ A∞. We study the behaviour of the Ã∞-constant under the operator already considered by Johnson and Neugebauer [18] and establish the equivalence of the two constants G̃1(Jf ) and Ã∞(Jf-1). Our quantitative esti-mates are sharp}