Let VMOF denote the closure of Cc∩Lip with respect to the seminorm ‖⋅‖BMOF, where F is a family of sections and the space BMOF associated to the family F was introduced by Caffarelli and Gutiérrez (1996) . Sections play an important role in the investigation of Monge–Ampère equation and the linearized Monge–Ampère equation. We show that the dual of VMOF is the Hardy space HF 1 defined in Ding and Lin (2005) . As an application, we prove that μ-almost everywhere convergence of a sequence of functions bounded in HF 1 to a function in L1(dμ) implies the weak* convergence.
|頁（從 - 到）||463-476|
|期刊||Journal of Mathematical Analysis and Applications|
|出版狀態||已出版 - 1 11月 2017|