Authors’ abstract: Some new refined multidimensional Hardy-type inequalities for
and their duals are derived and discussed. Moreover, these inequalities hold in the reverse direction when
. 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.