Abstract
An explicit representation is given to the remainder of a critical Hardy inequality in \({L^{n}(\mathbb{R}^{n})}\) with \({n \ge 2}\).
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References
Adimurthi, Chaudhuri N., Ramaswamy M.: An improved Hardy-Sobolev inequality and its application. Proc. Amer. Math. Soc. 130, 489–505 (2002)
Adimurthi, Chaudhuri N., Sandeep K.: Existence and non-existence of the first eigenvalue of the perturbed Hardy-Sobolev operator. Proc. Roy. Edinburgh A 132, 1021–1043 (2002)
N. Ioku and M. Ishiwata, A scale invariant form of a critical Hardy inequality, Int. Math. Res. Notices (2014), doi:10.1093/imrn/rnu212, 17pages.
N. Ioku, M. Ishiwata, and T. Ozawa, Sharp remainder terms of Hardy type inequalities in L p, preprint, 2015.
Machihara S., Ozawa T., Wadade H.: Hardy type inequalities on balls. Tohoku Math. J. 65, 321–330 (2013)
S. Machihara, T. Ozawa, and H. Wadade, On the Hardy type inequalities, preprint, 2015.
Takahashi F.: A simple proof of Hardy’s inequality in a limiting case, Arch. Math. 104, 77–82 (2015)
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Ioku, N., Ishiwata, M. & Ozawa, T. Sharp remainder of a critical Hardy inequality. Arch. Math. 106, 65–71 (2016). https://doi.org/10.1007/s00013-015-0841-7
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DOI: https://doi.org/10.1007/s00013-015-0841-7