桃園中壢地區數學期刊圖書服務計畫; Mathematics Research Promotion Center, Library Service Project (Taoyuan Area)

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/25452

Title:	桃園中壢地區數學期刊圖書服務計畫;Mathematics Research Promotion Center, Library Service Project (Taoyuan Area)
Authors:	許正雄;傅承德
Contributors:	數學系
Keywords:	數學類
Date:	2010-12-01
Issue Date:	2010-06-04 11:01:14 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	本計畫中，我們考慮海森堡群上的Schrodinger算子nHnLV=?Δ+H, 其中nΔH是sub-Laplacian, V是滿足逆Holder?等式的一個位勢。我們研究關於Schrodinger算子L所衍生的哈地空間與其對偶空間. 1(nLHH ()nLBMOH 我們打算用半群極大函??定義，然後證明上的原子分解及Riesz 變換刻畫。緊接著?用變形的sharp函??定義，然後證明函?的Fefferman-Stein分解與Carleson測?刻畫，及證明的對偶空間就是. 1(nLHH1(nLHH(nLBMOH()nLBMOH1(nLHH()nLBMOH 最後，我們將證明一些算子在上的有界性，其中包括：伴隨Riesz變換、Littlewood-Paley g-函?、Lusin面積函?、Hardy-Littlewood極大函?、與半群極大函?等。 In this proposal, we consider the Schrodinger operator nLV=?Δ+H on the Heisenberg group , where is the sub-Laplacian and the nonnegative potential V belongs to the reverse Holder class. We investigate the Hardy space associated with the Schrodinger operator L and its dual space . nHnΔH1(nLHH ()nLBMOH We will define in terms of the maximal function with respect to the semigroup , and give the atomic decomposition of . As an application of the atomic decomposition theorem, we prove that can be characterized by the Riesz transforms associated with L. 1(nLHH{:0}sLes?>1(nLHH1(nLHH We define by means of a revised sharp function related to the potential V. We give the Fefferman-Stein type decomposition of -functions with respect to the (adjoint) Riesz transforms for L, and characterize in terms of the Carleson measure. Then we will show the dual space of to be . (nLBMOH(nLBMOH(nLBMOH1(nLHH()nLBMOH Finally, we are going to establish the -boundedness of some operators, such as the (adjoint) Riesz transforms, the Littlewood-Paley g-function, the Lusin area integral, the Hardy-Littlewood maximal function, and the semigroup maximal function. 研究期間：9901 ~ 9912
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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