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arXiv · 2503.19895

A Herglotz-Nevanlinna function from the optimal discrete $p$-Hardy weight

František Štampach·Jakub Waclawek
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Abstract

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 $\omega_{p}$ was determined therein. We prove that $\omega_{p}$ 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.

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František Štampach, Jakub Waclawek. 2025-03-25. A Herglotz-Nevanlinna function from the optimal discrete $p$-Hardy weight. https://arxiv.org/abs/2503.19895

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