Lacunary $δ$-Discretised Spherical Maximal Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912481147879424 |
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| author | Choudhary, Surjeet Singh Li, Ji Liang, Chong-Wei Shen, Chun-Yen |
| author_facet | Choudhary, Surjeet Singh Li, Ji Liang, Chong-Wei Shen, Chun-Yen |
| contents | We study the lacunary analogue of the $δ$-discretised spherical maximal operators introduced by Hickman and Jančar, for $δ\in (0, 1/2)$, and establish the boundedness on $L^p$ for all $1 < p < \infty$, along with the endpoint weak-type estimate $H^1 \to L^{1,\infty}$. We also prove the corresponding $L^p$ boundedness for the multi-parameter variant. The constants in these bounds are uniform in $δ$, and thus, by taking the limit $δ\to 0^+$, our results recover the classical boundedness of the lacunary spherical maximal function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lacunary $δ$-Discretised Spherical Maximal Operators Choudhary, Surjeet Singh Li, Ji Liang, Chong-Wei Shen, Chun-Yen Classical Analysis and ODEs We study the lacunary analogue of the $δ$-discretised spherical maximal operators introduced by Hickman and Jančar, for $δ\in (0, 1/2)$, and establish the boundedness on $L^p$ for all $1 < p < \infty$, along with the endpoint weak-type estimate $H^1 \to L^{1,\infty}$. We also prove the corresponding $L^p$ boundedness for the multi-parameter variant. The constants in these bounds are uniform in $δ$, and thus, by taking the limit $δ\to 0^+$, our results recover the classical boundedness of the lacunary spherical maximal function. |
| title | Lacunary $δ$-Discretised Spherical Maximal Operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2507.09962 |