spaces and Carleson measures for Schrödinger operators

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• 作者：Chin-Cheng Lin^a ; ¹ ; ^{clin@math.ncu.edu.tw"" rel=""nofollow} ; Heping Liu^b ; ² ; ^{hpliu@pku.edu.cn"" rel=""nofollow}
• 关键词：BMO space ; Carleson measure ; Hardy space ; Heisenberg group ; Reverse H&#xf6 ; lder class ; Schr&#xf6 ; dinger operator ; Stratified group
• 刊名：Advances in Mathematics
• 出版年：2011
• 出版时间：20 October 2011
• 年：2011
• 卷：228
• 期：3
• 页码：1631-1688
• 全文大小：371 K

文摘

Let be a Schrödinger operator on the Heisenberg group , where is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class . Here Q is the homogeneous dimension of . In this article we investigate the dual space of the Hardy-type space associated with the Schrödinger operator L, which is a kind of BMO-type space defined by means of a revised sharp function related to the potential V. We give the Fefferman–Stein type decomposition of BMO_L-functions with respect to the (adjoint) Riesz transforms for L, and characterize in terms of the Carleson measure. We also establish the BMO_L-boundedness of some operators, such as the (adjoint) Riesz transforms , the Littlewood–Paley function , the Lusin area integral , the Hardy–Littlewood maximal function, and the semigroup maximal function. All results hold for stratified groups as well.