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arXiv · 2404.00843

Landau's converse to H\" older's inequality

Melvyn B. Nathanson
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Abstract

By H\" older's inequality, if $\mathbf{x} \in \ell^p$, then $\mathbf{x}\mathbf{y} \in \ell^1$ for all $\mathbf{y} \in \ell^q$. Landau proved the converse result: If $\mathbf{x}\mathbf{y} \in \ell^1$ for all $\mathbf{y} \in \ell^q$, then $\mathbf{x} \in \ell^p$. This paper proves Landau's theorem and considers a related problem for Hilbert's inequality.

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Melvyn B. Nathanson. 2024-04-01. Landau's converse to H\" older's inequality. https://arxiv.org/abs/2404.00843

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