Merryfield's inequality for multiparameter martingales

Abstract

Abstract We extend an inequality of Merryfield, valid in the continuous setting, to discrete multiparameter martingales. As a consequence, we obtain the comparison of the maximal function with the square function: for regular multiparameter filtrations and . This estimate is new in the case of more than two parameters, and provides an alternative proof of Brossard's famous two‐parameter result.