摘要
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) [4]. 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) [8]. 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.
原文 | ???core.languages.en_GB??? |
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頁(從 - 到) | 463-476 |
頁數 | 14 |
期刊 | Journal of Mathematical Analysis and Applications |
卷 | 455 |
發行號 | 1 |
DOIs | |
出版狀態 | 已出版 - 1 11月 2017 |