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arXiv · 2606.09057

Weighted Hardy Inequality in $l_2$

Ivan Gadjev
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Abstract

We study the behaviour of the smallest possible constant $d_n$ in weighted Hardy inequality $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2 k^\epsilon\le d(n,\epsilon)\,\sum_{k=1}^{n}{a_k^2}\,k^\epsilon $$ The exact rate of convergence of $d_n$ is established and the ``almost extremal'' sequence is found.

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Ivan Gadjev. 2026-06-08. Weighted Hardy Inequality in $l_2$. https://arxiv.org/abs/2606.09057

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