Let f: Ω ⊂ R n → R n be a quasiconformal mapping whose Jacobian is denoted by J f and let E X P (Ω) be the space of exponentially integrable functions on Ω. We give an explicit bound for the norm of the composition operator T f: u E X P (Ω) → u ° f-1 E X P (f (Ω)) and, as a related question, we study the behaviour of the norm of log J f in the exponential class. The A ∞ property of J f is the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results.

Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class

GIOVA, Raffaella
2016

Abstract

Let f: Ω ⊂ R n → R n be a quasiconformal mapping whose Jacobian is denoted by J f and let E X P (Ω) be the space of exponentially integrable functions on Ω. We give an explicit bound for the norm of the composition operator T f: u E X P (Ω) → u ° f-1 E X P (f (Ω)) and, as a related question, we study the behaviour of the norm of log J f in the exponential class. The A ∞ property of J f is the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/55327
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact