Merryfield's inequality for multiparameter martingales

Guillermo Rey

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arXiv · 2506.02974

Merryfield's inequality for multiparameter martingales

Guillermo Rey

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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: \begin{align*} E[(Sf)^p] \lesssim E[(f^*)^p] \end{align*} for regular multiparameter filtrations and $0 < p < \infty$.

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BibTeX RIS

Guillermo Rey. 2025-06-03. Merryfield's inequality for multiparameter martingales. https://arxiv.org/abs/2506.02974

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