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

Nirmalendu Chaudhuri

doi:10.4171/zaa/1171

JournalszaaVol. 22, No. 4pp. 757–765

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

Nirmalendu Chaudhuri
Australian National University, Canberra, Australia

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Abstract

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 $2 \leq p < n$ is bounded by

\frac{p - 1}{p ^{2}} (\frac{n - p}{p})^{p - 2} \leq C \leq \frac{p - 1}{2} (\frac{n - p}{p})^{p - 2} .

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Nirmalendu Chaudhuri, Bounds for the Best Constant in an Improved Hardy-Sobolev Inequality. Z. Anal. Anwend. 22 (2003), no. 4, pp. 757–765

DOI 10.4171/ZAA/1171