$L^p$-improving bounds for spherical maximal operators over restricted dilation sets: radial improvement
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917867866292224 |
|---|---|
| author | Zhao, Shuijiang |
| author_facet | Zhao, Shuijiang |
| contents | In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two dimensions, sharp results are also obtained for quasi-Assouad regular sets $E$. A notable feature is that the high-dimensional results depend solely on the upper Minkowski dimension, while the two-dimensional results also involve other concepts in fractal geometry such as the Assouad spectrum. Additionally, the geometric shapes of the regions corresponding to the sharp $ L^p-$improving bounds differ significantly between the two cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p$-improving bounds for spherical maximal operators over restricted dilation sets: radial improvement Zhao, Shuijiang Classical Analysis and ODEs 42B25 In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two dimensions, sharp results are also obtained for quasi-Assouad regular sets $E$. A notable feature is that the high-dimensional results depend solely on the upper Minkowski dimension, while the two-dimensional results also involve other concepts in fractal geometry such as the Assouad spectrum. Additionally, the geometric shapes of the regions corresponding to the sharp $ L^p-$improving bounds differ significantly between the two cases. |
| title | $L^p$-improving bounds for spherical maximal operators over restricted dilation sets: radial improvement |
| topic | Classical Analysis and ODEs 42B25 |
| url | https://arxiv.org/abs/2412.09882 |