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2014 On the equivalence between some multidimensional Hardy-type inequalities
J.A. Oguntuase , L.-E. Persson, N. Samko, A. Sonubi
Banach J. Math. Anal. 8(1): 1-13 (2014). DOI: 10.15352/bjma/1381782082

Abstract

We prove and discuss some power weighted Hardy-type inequalities on finite and infinite sets. In particular, it is proved that these inequalities are equivalent because they can all be reduced to an elementary inequality, which can be proved by Jensen inequality. Moreover, the corresponding limit (Pólya--Knopp type) inequalities and equivalence theorem are proved. All constants in these inequalities are sharp.

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J.A. Oguntuase . L.-E. Persson. N. Samko. A. Sonubi. "On the equivalence between some multidimensional Hardy-type inequalities." Banach J. Math. Anal. 8 (1) 1 - 13, 2014. https://doi.org/10.15352/bjma/1381782082

Information

Published: 2014
First available in Project Euclid: 14 October 2013

zbMATH: 1280.26040
MathSciNet: MR3161677
Digital Object Identifier: 10.15352/bjma/1381782082

Subjects:
Primary: 26D15
Secondary: 26A51‎ , 47J20

Keywords: best constant , convexity , inequality , multidimensional Hardy-type inequalities , multidimensional Pólya--Knopp type inequalities , power weights

Rights: Copyright © 2014 Tusi Mathematical Research Group

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Vol.8 • No. 1 • 2014
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