整合研究：分析與最佳化-Monge-Ampere 奇異積分算子在 Triebel 空間的有界性;Monge-Ampere Singular Integral Operators Acting on Triebel-Lizorkin Spaces

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/82399

Title:	整合研究：分析與最佳化-Monge-Ampere 奇異積分算子在 Triebel 空間的有界性;Monge-Ampere Singular Integral Operators Acting on Triebel-Lizorkin Spaces
Authors:	林欽誠;陳中壹;黃大炎
Contributors:	國立中央大學數學系
Keywords:	子計畫一：Monge-Ampere 奇異積分算子;Triebel-Lizorkin 空間子計畫二：Besov空間;Holder空間;Monge-Apere 奇異積分算子;子計畫一：Monge-Ampere singular integral operators;Triebel-Lizorkin spaces子計畫二：Besov space;Holder space;Monge-Apere singular integral operators
Date:	2020-01-13
Issue Date:	2020-01-13 14:50:40 (UTC+8)
Publisher:	科技部
Abstract:	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.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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