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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.03465 |
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Table of Contents:
- In his influential 1986 paper, Rubio de Francia established $L^p$ bounds for the maximal function generated by dilations of measures $μ$ whose Fourier transforms $\widehatμ$ satisfy specific decay condition. In the present work, we obtain results that complement his work in several directions. In particular, we obtain restricted weak-type endpoint bound on the maximal function and $L^p$--$L^q$ bounds on its local variant. We also investigate how Frostman's growth condition on the measure influences those maximal bounds. While a key feature of Rubio de Francia's result is that $L^p$ boundedness is determined solely by the decay order of $\widehatμ$, we show that the Frostman condition plays a significant role when the growth order exceeds $d-1$ or when $L^p$--$L^q$ estimates are considered.