A1 Journal article (refereed)
The Qα-restriction problem (2019)

Wang, Z., Xiao, J., & Zhou, Y. (2019). The Qα-restriction problem. Asian Journal of Mathematics, 23(5), 837-876. https://doi.org/10.4310/AJM.2019.v23.n5.a4

JYU authors or editors

Publication details

All authors or editors: Wang, Z.; Xiao, J.; Zhou, Y.

Journal or series: Asian Journal of Mathematics

ISSN: 1093-6106

eISSN: 1945-0036

Publication year: 2019

Volume: 23

Issue number: 5

Pages range: 837-876

Publisher: International Press

Publication country: United States

Publication language: English

DOI: https://doi.org/10.4310/AJM.2019.v23.n5.a4

Publication open access: Not open

Publication channel open access:


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].

Free keywords: Q space; restriction; Ahlfors regular domain; uniform domain; Minkowski type dimension

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 1

Last updated on 2021-07-07 at 21:39