A decomposition for Hardy martingales Paul Muller 60G42 60G46 32A35Hardy MartingalesMartingale Inequalitiescomplex convexity We prove a decomposition for Hardy martingales that strengthen its square function characterization. We apply the underlying method to several well-known martingale inequalities, for which we obtain new proofs. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4796 10.1512/iumj.2012.61.4796 en Indiana Univ. Math. J. 61 (2012) 1801 - 1816 state-of-the-art mathematics http://iumj.org/access/