Sharp inequalities between L^p-norms for the higher dimensional Hardy operator and its dual

Abstract

. We derive the two-sided inequalities between L p ( X ) -norms ( 1 < p < ∞ ) of the higher dimensional Hardy operator and its dual, where the underlying space X is the Heisenberg group H n or the Euclidean space R n . The interest of main results is that it relates two-sided inequalities with sharp constants which are dimension free. The methodology is completely depending on the rotation method.