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Theoretical analysis demonstrates Merryfield's inequality for discrete multiparameter martingales, extending maximal and square function comparisons to higher dimensions.
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.
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