Abstract
The aim of this note is to derive the Rellich type inequality for Schrödinger operators with singular potential of the inverse-square type. In general, the standard Rellich inequality holds in the case of the space dimensions n is larger than 5. It seems interesting that the inequality still holds by perturbing the minus Laplacian by means of inverse-square positive potential even if n = 3, 4.
Dedicated to Professor Tohru Ozawa on his 60th birthday
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Acknowledgements
The first author was supported in part by INDAM, GNAMPA—Gruppo Nazionale per l’Analisi Matematica, la Probabilita e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, by Top Global University Project, Waseda University, by the project PRIN 2020XB3EFL with the Italian Ministry of Universities and Research and the Project PRA 2022 85 of University of Pisa. The second author was partially supported by Grant-in-Aid for Science Research (No.16H06339, No. 19H01795, and No. 22H00097), JSPS
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Georgiev, V., Kubo, H. (2022). On the Rellich Type Inequality for Schrödinger Operators with Singular Potential. In: Ruzhansky, M., Wirth, J. (eds) Harmonic Analysis and Partial Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-24311-0_5
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