Carleson measures, BMO spaces and balayages associated to Schr(o)dinger operators

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（11）
• 页码范围: 2077-2092
• 页数: 16页
• 语种: 英文
• DOI: 10.1007/s11425-016-9147-y

摘要

Let L be a Schr(o)dinger operator of the form L =-A + V acting on L2(Rn),n≥ 3,where the non-negative potential V belongs to the reverse H(o)lder class Bq for some q ≥ n.Let BMOL(Rn) denote the BMO space associated to the Schr(o)dinger operator L on Rn.In this article,we show that for every f ∈ BMOz(Rn)with compact support,then there exist g ∈ L∞(Rn) and a finite Carleson measure μ such that f(x) =g(x) + Sμ,p(x)with ||9||∞ + |||μ|||t ≤ C||f||BMOz(Rn),where Sμ,p =fRn+1 Pt(x,y)dμ(y,t),and Pt(x,y) is the kernel of the Poisson semigroup [e-t√L]t＞0 on L2(Rn).Conversely,if μ is a Carleson measure,then Sμ,p belongs to the space BMOL(Rn).This extends the result for the classical John-Nirenberg BMO space by Carleson (1976) (see also Garnett and Jones (1982),Uchiyama (1980) and Wilson (1988)) to the BMO setting associated to Schr(o)dinger operators.