Abstract
We consider Hardy inequalities on antisymmetric functions. Such inequalities have substantially better constants. We show that they depend on the lowest degree of an antisymmetric harmonic polynomial. This allows us to obtain some Caffarelli–Kohn–Nirenberg-type inequalities that are useful for studying spectral properties of Schrödinger operators.
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Acknowledgments
The authors would like to express their gratitude to J. Dolbeault, M. J. Esteban, R. Frank, and A. Ilyin for useful discussions.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 55–64 https://doi.org/10.4213/faa3873.
To Mikhail Zakharovich Solomyak, a colleague and the teacher, with respect and admiration
Translated by A. Laptev
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Hoffmann-Ostenhof, T., Laptev, A. Hardy Inequality for Antisymmetric Functions. Funct Anal Its Appl 55, 122–129 (2021). https://doi.org/10.1134/S0016266321020040
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DOI: https://doi.org/10.1134/S0016266321020040