2019

Wang, Z.; Xiao, J.; Zhou, Y.

Let α∈[0,1) and Ω be an open connected subset of Rn≥2. This paper shows that the Qα-restriction problem Qα|Ω=Qα(Ω) is solvable if and only if Ω is an Ahlfors n-regular domain; i.e., vol(B(x,r)∩Ω)≳rn for any Euclidean ball B(x,r) with center x∈Ω and radius r∈(0,diam(Ω)) , thereby not only yielding an exponential Qα-integrability as a proper adjustment of the John–Nirenberg type inequality for Qα conjectured in [3, Problem 8.1, (8.2)] but also resolving the quasiconformal extension problem for Qα posed in [3, Problem 8.5].