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不等式的一個位勢。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數來定義，然後證明上的原子分解及Riesz 變換刻畫。緊接著利用變形的sharp函數來定義，然後證明函數的Fefferman-Stein分解與Carleson測度刻畫，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-函數、Lusin面積函數、Hardy-Littlewood極大函數、與半群極大函數等。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：9908 ~ 10007
