Spherical maximal functions and Hardy spaces for Fourier integral operators
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915809956200448 |
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| author | Ghosh, Abhishek Liu, Naijia Rozendaal, Jan Song, Liang |
| author_facet | Ghosh, Abhishek Liu, Naijia Rozendaal, Jan Song, Liang |
| contents | We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds extend to general hypersurfaces with non-vanishing Gaussian curvature, to the complex spherical means, and to geodesic spheres on compact manifolds. We also obtain improved maximal function bounds and pointwise convergence statements for wave equations, both on $\mathbb{R}^{n}$ and on compact manifolds. The maximal function bounds are essentially sharp for all $p\in[1,2]\cup [\frac{2(n+1)}{n-1},\infty)$, for each such hypersurface, every complex spherical mean, and on every manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical maximal functions and Hardy spaces for Fourier integral operators Ghosh, Abhishek Liu, Naijia Rozendaal, Jan Song, Liang Classical Analysis and ODEs Analysis of PDEs Primary 42B25. Secondary 42B35, 42B37, 58J40 We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds extend to general hypersurfaces with non-vanishing Gaussian curvature, to the complex spherical means, and to geodesic spheres on compact manifolds. We also obtain improved maximal function bounds and pointwise convergence statements for wave equations, both on $\mathbb{R}^{n}$ and on compact manifolds. The maximal function bounds are essentially sharp for all $p\in[1,2]\cup [\frac{2(n+1)}{n-1},\infty)$, for each such hypersurface, every complex spherical mean, and on every manifold. |
| title | Spherical maximal functions and Hardy spaces for Fourier integral operators |
| topic | Classical Analysis and ODEs Analysis of PDEs Primary 42B25. Secondary 42B35, 42B37, 58J40 |
| url | https://arxiv.org/abs/2401.16955 |