Abstract
The purpose of this paper is to prove L p-boundedness of an operator φ(H V ), where \(H_{V } = -\Delta + V (x)\) is the Schrödinger operator on an open set \(\Omega \) of \(\mathbb{R}^{d}\) (d ≥ 1). Moreover, we prove uniform L p-estimates for φ(θ H V ) with respect to a parameter θ > 0. This paper will give an improvement of our previous paper (Iwabuchi et al., L p-mapping properties for Schrödinger operators in open sets of \(\mathbb{R}^{d}\), submitted); assumptions of potential V and space dimension.
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Acknowledgements
The first author was supported by JSPS Grant-in-Aid for Young Scientists (B) (No. 25800069), Japan Society for the Promotion of Science. The second author was supported by Grant-in-Aid for Scientific Research (C) (No. 15K04967), Japan Society for the Promotion of Science.
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Iwabuchi, T., Matsuyama, T., Taniguchi, K. (2017). L p-boundedness of Functions of Schrödinger Operators on an Open Set of \(\mathbb{R}^{d}\) . In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_39
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DOI: https://doi.org/10.1007/978-3-319-48812-7_39
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