Refined multidimensional hardy-type inequalities via superquadracity

Abstract

Some new refined multidimensional Hardy-type inequalities for p ≥ 2 and their duals are derived and discussed. Moreover, these inequalities hold in the reversed direction when 1 < ≤ 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, Refnement of Hardy’s inequalities via superquadratic and subquadratic functions, J. Math. Anal. Appl., 339 (2008), no. 2, 1305– 1312] to a multidimensional setting