Vector-valued estimates for shifted operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914661037768704 |
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| author | Park, Bae Jun |
| author_facet | Park, Bae Jun |
| contents | Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear multipliers, and multilinear rough singular integrals. Estimates for such shifted operators have a certain logarithmic growth in terms of the shift factor, but the optimality of the logarithmic growth has not yet been fully resolved. In this article, we provide sharp vector-valued shifted maximal inequality for generalized Peetre's maximal function, from which improved estimates for the above shifted operators follow with optimal logarithmic growths in a new way. We also obtain a vector-valued maximal inequality for the shifted (dyadic) Hardy-Littlewood maximal operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vector-valued estimates for shifted operators Park, Bae Jun Classical Analysis and ODEs Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear multipliers, and multilinear rough singular integrals. Estimates for such shifted operators have a certain logarithmic growth in terms of the shift factor, but the optimality of the logarithmic growth has not yet been fully resolved. In this article, we provide sharp vector-valued shifted maximal inequality for generalized Peetre's maximal function, from which improved estimates for the above shifted operators follow with optimal logarithmic growths in a new way. We also obtain a vector-valued maximal inequality for the shifted (dyadic) Hardy-Littlewood maximal operator. |
| title | Vector-valued estimates for shifted operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.17785 |