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arXiv · 1802.04411

Poincar\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube

Dong Li·Alexander Volberg
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Abstract

We prove here some dimension free Poincar\'e-type inequalities on Hamming cube for functions with different spectral properties and for fractional Laplacians. In this note the main attention is paid to estimates in $L^1$ norm on Hamming cube. We build the examples showing that our assumptions on spectral properties of functions cannot be dropped in general.

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Dong Li, Alexander Volberg. 2018-02-13. Poincar\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube. https://arxiv.org/abs/1802.04411

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