Clarkson-McCarthy Inequality on a Locally Compact Group

Abstract

Let G be a locally compact group, μ its Haar measure, G^ its Pontryagin dual and ν the dual measure. For any Aθ∈L1(G;Cp)∩L2(G;Cp), (Cp is Schatten ideal), and 1<p≤2 we prove (Formula presented.) where q=p/(p-1). This appears to be a generalization of some earlier obtained inequalities, including Clarkson-McCarthy inequalities (in the case G=Z2) and Hausdorff-Young inequality. Some corollaries are also given.