子計畫一：探討由 section 族所衍生的 Triebel 空間，然後證明：Monge-Ampere 奇異積分算子作用在 Triebel 空間上的有界性。子計畫二：在測度只滿足雙倍條件下，我們建立一套關於quasi-metric 球相關的Besov空間。我們也定義了此種Holder空間並給出此空間與某些Besov空間的對偶空間等價。作為一個應用，我證明了Monge-Apere 奇異積分算子在這兩種空間上有界。 ;子計畫一：We study the Triebel-Lizorkin spaces associated with sections which are closely related to the Monge-Ampere equations, and show that Monge-Ampere singular integral operators are bounded on these Triebel-Lizorkin spaces.子計畫二：We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on measure. We introduce the corresponding Holder spaces as well, and show that the dual of some Besov spaces defined here are equivalent to the corresponding Holder spaces. As an application, we show that Monge-Ampere singular integral operators are bounded on these spaces.
