Survey on bilinear spherical averages and associated maximal operators
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915826273091584 |
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| author | Borges, Tainara |
| author_facet | Borges, Tainara |
| contents | In this survey, we collect recent progress in the understanding of $L^{p}$ bounds for bilinear spherical averages and some associated maximal functions like the bilinear spherical maximal function and its lacunary counterpart. We describe necessary conditions satisfied by triples in the $L^{p}$ improving region of a bilinear spherical averaging operator and the localized bilinear spherical maximal function, as well as describe the best-known boundedness regions to date. We state some open questions along the way to motivate future research on this topic, and we exploit some possible generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Survey on bilinear spherical averages and associated maximal operators Borges, Tainara Classical Analysis and ODEs 42B15, 42B25 In this survey, we collect recent progress in the understanding of $L^{p}$ bounds for bilinear spherical averages and some associated maximal functions like the bilinear spherical maximal function and its lacunary counterpart. We describe necessary conditions satisfied by triples in the $L^{p}$ improving region of a bilinear spherical averaging operator and the localized bilinear spherical maximal function, as well as describe the best-known boundedness regions to date. We state some open questions along the way to motivate future research on this topic, and we exploit some possible generalizations. |
| title | Survey on bilinear spherical averages and associated maximal operators |
| topic | Classical Analysis and ODEs 42B15, 42B25 |
| url | https://arxiv.org/abs/2502.02765 |