{"paper":{"title":"Poincar\\'e type and spectral gap inequalities with fractional Laplacians on Hamming cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Dong Li","submitted_at":"2018-02-13T00:46:21Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04411","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}