Sparse Bounds for Discrete Maximal Functions associated with Birch-Magyar averages
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arXiv
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| Format: | Preprint |
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2024
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| author | Bhojak, Ankit Choudhary, Surjeet Singh Samanta, Siddhartha Shrivastava, Saurabh |
| author_facet | Bhojak, Ankit Choudhary, Surjeet Singh Samanta, Siddhartha Shrivastava, Saurabh |
| contents | In this article, we study discrete maximal function associated with the Birch-Magyar averages over sparse sequences. We establish sparse domination principle for such operators. As a consequence, we obtain $\ell^p$-estimates for such discrete maximal function over sparse sequences for all $p>1$. The proof of sparse bounds is based on scale-free $\ell^p-$improving estimates for the single scale Birch-Magyar averages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Bounds for Discrete Maximal Functions associated with Birch-Magyar averages Bhojak, Ankit Choudhary, Surjeet Singh Samanta, Siddhartha Shrivastava, Saurabh Number Theory Classical Analysis and ODEs Primary 11D72, 42B25, Secondary 11P55, 11L05 In this article, we study discrete maximal function associated with the Birch-Magyar averages over sparse sequences. We establish sparse domination principle for such operators. As a consequence, we obtain $\ell^p$-estimates for such discrete maximal function over sparse sequences for all $p>1$. The proof of sparse bounds is based on scale-free $\ell^p-$improving estimates for the single scale Birch-Magyar averages. |
| title | Sparse Bounds for Discrete Maximal Functions associated with Birch-Magyar averages |
| topic | Number Theory Classical Analysis and ODEs Primary 11D72, 42B25, Secondary 11P55, 11L05 |
| url | https://arxiv.org/abs/2412.06348 |