The Bellman Function for Level Sets of Sparse Operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866910051031056384 |
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| author | Fay, Irina Holmes Pence, Zachary H. Small, John Freeland Zhou, Xiaokun |
| author_facet | Fay, Irina Holmes Pence, Zachary H. Small, John Freeland Zhou, Xiaokun |
| contents | We investigate weak-type $(1, 1)$ boundedness of sparse operators with respect to Lebesgue measure. Specifically, we find the Bellman function maximizing level sets of sparse operators (localized to an interval) and use this to find the exact weak-$(1,1)$ norm of these sparse operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Bellman Function for Level Sets of Sparse Operators Fay, Irina Holmes Pence, Zachary H. Small, John Freeland Zhou, Xiaokun Classical Analysis and ODEs We investigate weak-type $(1, 1)$ boundedness of sparse operators with respect to Lebesgue measure. Specifically, we find the Bellman function maximizing level sets of sparse operators (localized to an interval) and use this to find the exact weak-$(1,1)$ norm of these sparse operators. |
| title | The Bellman Function for Level Sets of Sparse Operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2506.12315 |