An Exact Upper Bound on the L^p Lebesgue Constant and The ∞-Rényi Entropy Power Inequality for Integer Valued Random Variables

08/23/2018

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by   Peng Xu, et al.

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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> 2. As an application, we also verified the implication of a new ∞ -Rényi entropy power inequality for integer valued random variables.