A fractal local smoothing problem for the wave equation
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915714529492992 |
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| author | Beltran, David Roos, Joris Rutar, Alex Seeger, Andreas |
| author_facet | Beltran, David Roos, Joris Rutar, Alex Seeger, Andreas |
| contents | For any given set $E\subset [1,2]$, we discuss a fractal frequency-localized version of the $L^p$ local smoothing estimates for the half-wave propagator with times in $E$. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of $E$ and the Legendre transform. We validate the conjecture for radial functions. We also prove a similar result for fractal-time $L^2\to L^q$ and square function bounds, for arbitrary $L^2$ functions and general time sets. We formulate a conjecture for $L^p\to L^q$ generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fractal local smoothing problem for the wave equation Beltran, David Roos, Joris Rutar, Alex Seeger, Andreas Classical Analysis and ODEs Analysis of PDEs 35L05, 42B20, 28A80 For any given set $E\subset [1,2]$, we discuss a fractal frequency-localized version of the $L^p$ local smoothing estimates for the half-wave propagator with times in $E$. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of $E$ and the Legendre transform. We validate the conjecture for radial functions. We also prove a similar result for fractal-time $L^2\to L^q$ and square function bounds, for arbitrary $L^2$ functions and general time sets. We formulate a conjecture for $L^p\to L^q$ generalizations. |
| title | A fractal local smoothing problem for the wave equation |
| topic | Classical Analysis and ODEs Analysis of PDEs 35L05, 42B20, 28A80 |
| url | https://arxiv.org/abs/2501.12805 |