{"paper":{"title":"Shifts of a Measurable Function and Criterion of p-integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.GR"],"primary_cat":"math.FA","authors_text":"Boris Mityagin","submitted_at":"2016-08-28T22:10:45Z","abstract_excerpt":"It is shown that two conditions $f(a + \\cdot) - f(\\cdot) \\in L^p(R)$, and $(\\sin b \\cdot) f(\\cdot) \\in L^p(R)$ guarantee $f \\in L^p(R)$, $1 \\leq p < \\infty$, if and only if $ab$ is not in $(\\pi Z)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07860","kind":"arxiv","version":3},"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"}