Merryfield's inequality for multiparameter martingales
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912411525578752 |
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| author | Rey, Guillermo |
| author_facet | Rey, Guillermo |
| contents | 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 $0 < p < \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Merryfield's inequality for multiparameter martingales Rey, Guillermo Probability Classical Analysis and ODEs 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 $0 < p < \infty$. |
| title | Merryfield's inequality for multiparameter martingales |
| topic | Probability Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2506.02974 |