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Hardy Inequality for Antisymmetric Functions

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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Correspondence to T. Hoffmann-Ostenhof or A. Laptev.

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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

Keywords

  • Hardy inequalities
  • antisymmetric functions
  • Caffarelli–Kohn–Nirenberg inequality