2017/04/26 by Peng Chen, Chen, Peng, Xuan Thinh Duong +7
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1704.07997
openalex publication_date 2017/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Ł be a Schrödinger operator of the form Ł=-Δ+V acting on L2(\mathbb Rn), n≥3, where the nonnegative potential V belongs to the reverse Hölder class Bq for some q≥ n. Let \rm BMOL(\RR) denote the BMO space associated to the Schrödinger operator Ł on \RR. In this article we show that for every f∈ \rm BMOL(\RR) with compact support, then there exist g∈ L∞(\RR) and a finite Carleson measure μ such that f(x)=g(x) + S_μ, \mathcal P(x) with ‖g‖∞ +‖|μ‖|c≤ C ‖f‖_\rm BMOL(\RR), where S_μ, \mathcal P=∫_\mathbb Rn+1+ \mathcal Pt(x,y) dμ(y, t), and \mathcal Pt(x,y) is the kernel of the Poisson semigroup \e-t√Ł\t> 0 on L2(\mathbb Rn). Conversely, if μ is a Carleson measure, then S_μ, \mathcal P belongs to the space \rm BMOL(\RR). This extends the result for the classical John--Nirenberg BMO space by Carleson \citeC (see also \citeU,GJ,W) to the BMO setting associated to Schrödinger operators.