Poincar\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube
Analysis of PDEs
2018-02-14 v1 Classical Analysis and ODEs
Probability
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 norm on Hamming cube. We build the examples showing that our assumptions on spectral properties of functions cannot be dropped in general.
Cite
@article{arxiv.1802.04411,
title = {Poincar\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube},
author = {Dong Li and Alexander Volberg},
journal= {arXiv preprint arXiv:1802.04411},
year = {2018}
}
Comments
11 pages