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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 4, 2003, pp. 757–765
DOI: 10.4171/ZAA/1171

Published online: 2003-12-31

Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality

Nirmalendu Chaudhuri[1]

(1) Australian National University, Canberra, Australia

We show that the best constant $C$ in the improved Hardy-Sobolev inequality of Adimurthi, N. Chaudhuri and M. Ramaswamy [Proc. Amer. Math. Soc. 130 (2002) 489–505] for $2 \le p < n$ is bounded by $$ {p - 1 \over p^2} \big({n - p \over p}\big)^{p-2} \le C \le {p - 1 \over 2} \Big({n - p \over p}\Big)^{p-2}.$$

Keywords: Hardy-Sobolev inequality, best constant

Chaudhuri Nirmalendu: Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality. Z. Anal. Anwend. 22 (2003), 757-765. doi: 10.4171/ZAA/1171