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An optimal improvement for the Hardy inequality on the hype..:

Berchio, Elvise ; Ganguly, Debdip ; Grillo, Gabriele.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics.  150 (2019)  4 - p. 1699-1736 , 2019
Link: https://doi.org/10.1017/prm.2018.139