Abstract
In this note, we obtain a simpler expression for the constant number given by Costin–Maz’ya on the sharp Hardy–Leray inequality for a class of solenoidal (namely divergence-free) vector fields, with respect to any radial power-weighted measure. The dependence of the constant on the weight exponent will be clear.
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Acknowledgements
This research was partly supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B) 19H01800 (F. Takahashi), and was also partly supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849).
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Hamamoto, N. A simpler expression for Costin–Maz’ya’s constant in the Hardy–Leray inequality with weight. Arch. Math. 116, 571–576 (2021). https://doi.org/10.1007/s00013-021-01595-z
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DOI: https://doi.org/10.1007/s00013-021-01595-z