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An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-Rényi Entropy Power Inequality for Integer Valued Random Variables (1808.07732v1)
Published 23 Aug 2018 in math.FA, cs.IT, math.IT, and math.PR
Abstract: In this paper, we proved an exact asymptotically sharp upper bound of the $Lp$ Lebesgue Constant (i.e. the $Lp$ 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.