On the weak* convergence in HF 1(Rn)

研究成果: 雜誌貢獻期刊論文同行評審

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???
頁(從 - 到)463-476
頁數14
期刊Journal of Mathematical Analysis and Applications
455
發行號1
DOIs
出版狀態已出版 - 1 11月 2017

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