In this paper we define the Hardy space Hℱ1 (Rn) associated with a family ℱ of sections and a doubling measure μ, where ℱ is closely related to the Monge-Ampère equation. Furthermore, we show that the dual space of Hℱ1 (Rn) is just the space BMOℱ(Rn), which was first defined by Caffarelli and Gutiérrez. We also prove that the Monge-Ampère singular integral operator is bounded from Hℱ1 (Rn) to L1(Rn, dμ).
|頁（從 - 到）||147-170|
|期刊||Tohoku Mathematical Journal|
|出版狀態||已出版 - 2005|