Small cap square function estimates
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914866613190656 |
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| author | Gan, Shengwen |
| author_facet | Gan, Shengwen |
| contents | We introduce small cap square function estimates for parabola and cone, and prove the sharp estimates. More precisely, we study the inequalities of form \[ \|f\|_p\le C_{α,p}(R) \Big\|(\sum_{γ\inΓ_α(R^{-1})}|f_γ|^2)^{1/2}\Big\|_p, \] where $Γ_α(R^{-1})$ is the set of small caps of width $R^{-α}$. We find the sharp constant $C_{α,p}(R)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small cap square function estimates Gan, Shengwen Classical Analysis and ODEs We introduce small cap square function estimates for parabola and cone, and prove the sharp estimates. More precisely, we study the inequalities of form \[ \|f\|_p\le C_{α,p}(R) \Big\|(\sum_{γ\inΓ_α(R^{-1})}|f_γ|^2)^{1/2}\Big\|_p, \] where $Γ_α(R^{-1})$ is the set of small caps of width $R^{-α}$. We find the sharp constant $C_{α,p}(R)$. |
| title | Small cap square function estimates |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2304.02816 |