Study of Bounded Variation on the H-L Nontangential Operator
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912292736598016 |
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| author | Toulson, Frederico |
| author_facet | Toulson, Frederico |
| contents | In this paper we present a proof of sharp boundedness of the discrete 1-dimensional Hardy-Littlewood nontangential maximal operator, when the parameter is in the range $[\frac{1}{3},+\infty)$. This generalizes a theorem by Bober, Carneiro, Hughes and Pierce, where they prove the same result for the uncentered version of the maximal operator. We also use analogous ideas to give an alternative proof for the continuous version of the theorem, by Ramos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Study of Bounded Variation on the H-L Nontangential Operator Toulson, Frederico Classical Analysis and ODEs In this paper we present a proof of sharp boundedness of the discrete 1-dimensional Hardy-Littlewood nontangential maximal operator, when the parameter is in the range $[\frac{1}{3},+\infty)$. This generalizes a theorem by Bober, Carneiro, Hughes and Pierce, where they prove the same result for the uncentered version of the maximal operator. We also use analogous ideas to give an alternative proof for the continuous version of the theorem, by Ramos. |
| title | Study of Bounded Variation on the H-L Nontangential Operator |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.19210 |