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Refined multidimensional Hardy-type inequalities via superquadracity. (English) Zbl 1165.26337
Authors’ abstract: Some new refined multidimensional Hardy-type inequalities for $p\ge 2$ and their duals are derived and discussed. Moreover, these inequalities hold in the reverse direction when $1 < p\le 2$. The results obtained are based mainly on some new results for superquadratic and subquadratic functions. In particular, the results further extend recent ones in [{\it J. A. Oguntuase} and {\it L.-E. Persson}, J. Math. Anal. Appl., 339, No. 2, 1305--1312 (2008; Zbl 1131.26014)] to a multidimensional setting.

26D15Inequalities for sums, series and integrals of real functions
26A51Convexity, generalizations (one real variable)
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