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arXiv · 1808.07732

An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-R\'enyi Entropy Power Inequality for Integer Valued Random Variables

Peng Xu·Mokshay Madiman·James Melbourne
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Abstract

In this paper, we proved an exact asymptotically sharp upper bound of the $L^p$ Lebesgue Constant (i.e. the $L^p$ norm of Dirichlet kernel) for $p\ge 2$. As an application, we also verified the implication of a new $\infty $-R\'enyi entropy power inequality for integer valued random variables.

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Peng Xu, Mokshay Madiman, James Melbourne. 2018-08-23. An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-R\'enyi Entropy Power Inequality for Integer Valued Random Variables. https://arxiv.org/abs/1808.07732

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