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Hardy and Sobolev inequalities on antisymmetric functions

    https://doi.org/10.1142/S1664360723500108Cited by:1 (Source: Crossref)

    We obtain sharp Hardy inequalities on antisymmetric functions, where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the paper [Th. Hoffmann-Ostenhof and A. Laptev, Hardy inequalities with homogeneous weights, J. Funct. Anal. 268 (2015) 3278–3289], where Hardy’s inequalities were considered for the antisymmetric functions in the case of the 1D particles. As a byproduct we obtain some Sobolev and Gagliardo–Nirenberg type inequalities that are applied to the study of spectral properties of Schrödinger operators.

    Communicated by S. K. Jain

    AMSC: 35P15, 81Q10

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