He, Yuexiang; Wang, Yanhui Boundedness of Riesz operators related to Schrödinger operator on BMO type spaces. (Chinese. English summary) Zbl 1463.47061 Math. Pract. Theory 50, No. 4, 203-207 (2020). Summary: Let \(\mathcal{L} = -\Delta + V\) be the Schrödinger operator and the nonnegative potential \(V\) belong to the reverse Hölder class \(RH_s\) with \(s > n/2\). In this paper, we prove that the Riesz operator \({T_\alpha} = \mathcal{L}^{-\alpha}V^\alpha\) is bounded on the BMO type space \(BMO_{\mathcal{L}} (\mathbb{R}^n)\). As an application, we get the boundedness of operator \(T_\alpha^* = {V^\alpha}{\mathcal{L}^{-\alpha}}\) on Hardy type space \(H_\mathcal{L}^1 (\mathbb{R}^n)\). These results generalize substantially some well-known results. MSC: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators 30H35 BMO-spaces Keywords:Schrödinger operator; reverse Hölder class; BMO space; Hardy space PDFBibTeX XMLCite \textit{Y. He} and \textit{Y. Wang}, Math. Pract. Theory 50, No. 4, 203--207 (2020; Zbl 1463.47061)