Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 785-796
Università degli Studi di Napoli Federico II, Dipartimento di
Matematica e Applicazioni "R. Caccioppoli"
Via Cintia, 80126 Napoli, Italy; fernando.farroni 'at' unina.it
Università degli Studi di Napoli "Parthenope",
Dipartimento di Statistica e Matematica per la Ricerca Economica
Palazzo Pakanowsky, Via Generale Parisi 13,
80132 Napoli, Italy; raffaella.giova 'at' uniparthenope.it
Abstract. Let f : Rn -> Rn be a quasiconformal mapping whose Jacobian is denoted by Jf and let A\infty be the Muckenhoupt class of weights w satisfying
(\averageintB w dx) (exp \averageintB log 1/w dx) \le A,
for every ball B \subset Rn and for some positive constant A \ge 1 independent of B. We consider two characteristic constants Ã\infty(w) and ~G1(w) which are simultaneously finite for every w \in A\infty. We study the behaviour of the Ã\infty-constant under the operator already considered by Johnson and Neugebauer [18]
w \in A\infty \mapsto (w o f) Jf \in A\infty,
and establish the equivalence of the two constants ~G1(Jf) and Ã\infty(Jf-1). Our quantitative estimates are sharp.
2010 Mathematics Subject Classification: Primary 42B25, 46E30, 47B33.
Key words: Muckenhoupt weights, composition operators, sharp estimates.
Reference to this article: F. Farroni and R. Giova: Change of variables for A\infty weights by means of quasiconformal mappings: sharp results. Ann. Acad. Sci. Fenn. Math. 38 (2013), 785-796.
doi:10.5186/aasfm.2013.3852
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