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 ~ Ã<sub/> (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.

### Change of variables for $A_\infty$ weights by means of quasiconformal mappings: sharp results

#### Abstract

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 ~ Ã (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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/28618
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