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arXiv · 2603.21252

A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$

Samson Owusu-Ensaw·Benoit F. Sehba·Ransford T. Tweneboanah
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Abstract

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.

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Samson Owusu-Ensaw, Benoit F. Sehba, Ransford T. Tweneboanah. 2026-03-22. A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$. https://arxiv.org/abs/2603.21252

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