BMOL(H{double-struck}n) spaces and Carleson measures for Schrödinger operators

Chin Cheng Lin, Heping Liu

研究成果: 雜誌貢獻期刊論文同行評審

48 引文 斯高帕斯(Scopus)


Let L=-ΔH{double-struck}n+V be a Schrödinger operator on the Heisenberg group H{double-struck}n, where ΔH{double-struck}n is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class BQ2. Here Q is the homogeneous dimension of H{double-struck}n. In this article we investigate the dual space of the Hardy-type space HL1(H{double-struck}n) associated with the Schrödinger operator L, which is a kind of BMO-type space BMOL(H{double-struck}n) defined by means of a revised sharp function related to the potential V. We give the Fefferman-Stein type decomposition of BMOL-functions with respect to the (adjoint) Riesz transforms R̃jL for L, and characterize BMOL(H{double-struck}n) in terms of the Carleson measure. We also establish the BMOL-boundedness of some operators, such as the (adjoint) Riesz transforms R̃jL, the Littlewood-Paley function sQL, the Lusin area integral SQL, the Hardy-Littlewood maximal function, and the semigroup maximal function. All results hold for stratified groups as well.

頁(從 - 到)1631-1688
期刊Advances in Mathematics
出版狀態已出版 - 20 10月 2011


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