arXiv 1802.044112018-02-13math.APmath.CAmath.PR

Poincaré type and spectral gap inequalities with fractional Laplacians on Hamming cube

Dong Li, Alexander Volberg

备注：: 11 pages

英文摘要：

We prove here some dimension free Poincaré-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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