2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149480We extend ideas of Garling to consider the so called Hardy martingales in a more general setting of H^p theory of compact abelian groups with ordered dual. As a consequence, we obtain a new proof of a result of Helson and Lowdenslager which generalizes Jensen's Inequality for H^1 functions.Functional Analysis43A17text