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arXiv · 2503.11869

On the optimal $L_p$-$L_4$ Khintchine inequality

Adam Barański·Daniel Murawski·Piotr Nayar·Krzysztof Oleszkiewicz
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Abstract

We derive optimal dimension independent constants in the classical Khintchine inequality between the $p$th and fourth moment for $p\ge 4$. As an application we deduce stability estimates for the Khintchine inequality between the $p$th and second moment for $p \geq 4$.

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Adam Barański, Daniel Murawski, Piotr Nayar, Krzysztof Oleszkiewicz. 2025-03-14. On the optimal $L_p$-$L_4$ Khintchine inequality. https://arxiv.org/abs/2503.11869

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