Banach Journal of Mathematical Analysis

Refined Multidimensional Hardy-type inequalities via superquadracity

J. A. Oguntuase, L.-E. Persson, E. K. Essel, and B. A. Popoola

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Some new refined multidimensional Hardy-type inequalities for $p\geq 2$ and their duals are derived and discussed. Moreover, these inequalities hold in the reversed direction when $p \neq 1, 1\leq p\leq 2.\ $The results obtained are based mainly on some new results for superquadratic and subquadratic functions. In particular, our results further extend the recent results in [J.A. Oguntuase and L.-E. Persson, Refinement of Hardy's inequalities via superquadratic and subquadratic functions, J. Math. Anal. Appl., 339 (2008), no. 2, 1305-1312] to a multidimensional setting.

Article information

Banach J. Math. Anal. Volume 2, Number 2 (2008), 129-139.

First available in Project Euclid: 21 April 2009

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Zentralblatt MATH identifier

Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 26A51: Convexity, generalizations

multidimensional Hardy-type inequalities refined Hardy's inequalities dual inequalities superquadratic functions subquadratic functions


Oguntuase, J. A.; Persson, L.-E.; Essel, E. K.; Popoola, B. A. Refined Multidimensional Hardy-type inequalities via superquadracity. Banach J. Math. Anal. 2 (2008), no. 2, 129--139. doi:10.15352/bjma/1240336299.

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