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.
|Titolo:||Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class|
|Data di pubblicazione:||2016|
|Appare nelle tipologie:||1.1 Articolo in rivista|