A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917356667666432 |
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| author | Owusu-Ensaw, Samson Sehba, Benoit F. Tweneboanah, Ransford T. |
| author_facet | Owusu-Ensaw, Samson Sehba, Benoit F. Tweneboanah, Ransford T. |
| contents | The Hardy operator is not bounded on the space of integrable functions on the positive half-line and its discrete counterpart on summable sequences. we introduce a modified Hardy operator obtained by subtracting a natural corrective term, and characterize the largest subspace of integrable functions on which this modified operator maps into integrable functions. The sharp condition is a logarithmic integrability (summability) requirement whose weight reflects obstructions on both small and large scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$ Owusu-Ensaw, Samson Sehba, Benoit F. Tweneboanah, Ransford T. Classical Analysis and ODEs Functional Analysis The Hardy operator is not bounded on the space of integrable functions on the positive half-line and its discrete counterpart on summable sequences. we introduce a modified Hardy operator obtained by subtracting a natural corrective term, and characterize the largest subspace of integrable functions on which this modified operator maps into integrable functions. The sharp condition is a logarithmic integrability (summability) requirement whose weight reflects obstructions on both small and large scales. |
| title | A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$ |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2603.21252 |