Multiparameter extensions of the Christ-Kiselev maximal theorem: strong variational bounds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912300269568000 |
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| author | Dabhi, Himali |
| author_facet | Dabhi, Himali |
| contents | For a linear operator $T$ bounded from $L^p(Y)$ to $L^q(X)$, the Christ-Kiselev theorem gives $L^p \to L^q$ bounds for the maximal function $T^{*}$ associated to filtrations on $Y$. This result has been extended by establishing bounds for the maximal function associated to a product of filtrations, also known as the multiparameter extension of the Christ-Kiselev theorem. In this note, we strengthen the multiparameter theorem by proving the $r$-variational bounds for the multiparameter trunctations when $r>p$. Furthermore, we replace $T$ by a multilinear operator to obtain a strong variational, multilinear, multiparameter extension of the Christ-Kiselev theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiparameter extensions of the Christ-Kiselev maximal theorem: strong variational bounds Dabhi, Himali Classical Analysis and ODEs 42B25, 37A46, 47B38 For a linear operator $T$ bounded from $L^p(Y)$ to $L^q(X)$, the Christ-Kiselev theorem gives $L^p \to L^q$ bounds for the maximal function $T^{*}$ associated to filtrations on $Y$. This result has been extended by establishing bounds for the maximal function associated to a product of filtrations, also known as the multiparameter extension of the Christ-Kiselev theorem. In this note, we strengthen the multiparameter theorem by proving the $r$-variational bounds for the multiparameter trunctations when $r>p$. Furthermore, we replace $T$ by a multilinear operator to obtain a strong variational, multilinear, multiparameter extension of the Christ-Kiselev theorem. |
| title | Multiparameter extensions of the Christ-Kiselev maximal theorem: strong variational bounds |
| topic | Classical Analysis and ODEs 42B25, 37A46, 47B38 |
| url | https://arxiv.org/abs/2503.22844 |