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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 \(p\geq 2\) and their duals are derived and discussed. Moreover, these inequalities hold in the reverse direction when \(1 < p\leq 2\). The results obtained are based mainly on some new results for superquadratic and subquadratic functions. In particular, the results further extend recent ones in [J. A. Oguntuase and L.-E. Persson, J. Math. Anal. Appl., 339, No. 2, 1305–1312 (2008; Zbl 1131.26014)] to a multidimensional setting.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations

Citations:

Zbl 1131.26014
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