A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$
Classical Analysis and ODEs
2026-03-24 v1 Functional Analysis
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.
Cite
@article{arxiv.2603.21252,
title = {A sharp logarithmic condition for the Hardy operator on $L^{1}(0,\infty)$ and $\ell^1$},
author = {Samson Owusu-Ensaw and Benoit F. Sehba and Ransford T. Tweneboanah},
journal= {arXiv preprint arXiv:2603.21252},
year = {2026}
}
Comments
10 pages