A Herglotz-Nevanlinna function from the optimal discrete $p$-Hardy weight
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| Format: | Preprint |
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2025
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| _version_ | 1866915213251444736 |
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| author | Štampach, František Waclawek, Jakub |
| author_facet | Štampach, František Waclawek, Jakub |
| contents | It was recently proved by Fischer, Keller, and Pogorzelski in [Integr. Equ. Oper. Theory, 95(24), 2023] that the classical discrete $p$-Hardy inequality admits an improvement, and the optimal $p$-Hardy weight $ω_{p}$ was determined therein. We prove that $ω_{p}$ directly corresponds to a Herglotz-Nevanlinna function, establish an integral representation for this function, and consequently confirm a slight modification of a conjecture on its absolute monotonicity from the aforementioned article. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Herglotz-Nevanlinna function from the optimal discrete $p$-Hardy weight Štampach, František Waclawek, Jakub Classical Analysis and ODEs Spectral Theory 30E20, 26D15, 26A48 It was recently proved by Fischer, Keller, and Pogorzelski in [Integr. Equ. Oper. Theory, 95(24), 2023] that the classical discrete $p$-Hardy inequality admits an improvement, and the optimal $p$-Hardy weight $ω_{p}$ was determined therein. We prove that $ω_{p}$ directly corresponds to a Herglotz-Nevanlinna function, establish an integral representation for this function, and consequently confirm a slight modification of a conjecture on its absolute monotonicity from the aforementioned article. |
| title | A Herglotz-Nevanlinna function from the optimal discrete $p$-Hardy weight |
| topic | Classical Analysis and ODEs Spectral Theory 30E20, 26D15, 26A48 |
| url | https://arxiv.org/abs/2503.19895 |