Merryfield's inequality for multiparameter martingales

2025/06/03 by Rey, Guillermo
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.02974

Abstract

We extend an inequality of Merryfield, valid in the continuous setting, to discrete multiparameter martingales. As a consequence, we obtain the L^p comparison of the maximal function with the square function: E[(Sf)^p] \lesssim E[(f^*)^p] for regular multiparameter filtrations and 0 < p < ∞.

Citations

• Characterizations of product Hardy spaces on stratified groups by singular integrals and maximal functions

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