Bilinear spherical maximal function with fractal dilations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911605143371776 |
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| author | Choudhary, Surjeet Singh Shen, Chun-Yen Shrivastava, Saurabh |
| author_facet | Choudhary, Surjeet Singh Shen, Chun-Yen Shrivastava, Saurabh |
| contents | In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski dimension of the set $E$. A particular case of this study, settles an open question of $L^p-$boundedness of the lacunary bilinear spherical maximal function at borderline cases $p_1=1$ or $p_2=1$ in dimension $d\geq3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear spherical maximal function with fractal dilations Choudhary, Surjeet Singh Shen, Chun-Yen Shrivastava, Saurabh Classical Analysis and ODEs 42B15, 42B25 In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski dimension of the set $E$. A particular case of this study, settles an open question of $L^p-$boundedness of the lacunary bilinear spherical maximal function at borderline cases $p_1=1$ or $p_2=1$ in dimension $d\geq3$. |
| title | Bilinear spherical maximal function with fractal dilations |
| topic | Classical Analysis and ODEs 42B15, 42B25 |
| url | https://arxiv.org/abs/2510.03094 |