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Boundedness of Riesz operators related to Schrödinger operator on BMO type spaces. (Chinese. English summary) Zbl 1463.47061

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
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