Banach Journal of Mathematical Analysis

Refined Multidimensional Hardy-type inequalities via superquadracity

Abstract

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

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

Dates
First available in Project Euclid: 21 April 2009

https://projecteuclid.org/euclid.bjma/1240336299

Digital Object Identifier
doi:10.15352/bjma/1240336299

Mathematical Reviews number (MathSciNet)
MR2436873

Zentralblatt MATH identifier
1165.26337

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

Citation

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. https://projecteuclid.org/euclid.bjma/1240336299