{"paper":{"title":"Compactness properties for modulation spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christine Pfeuffer, Joachim Toft","submitted_at":"2018-04-03T13:15:37Z","abstract_excerpt":"We prove that if $\\omega _1$ and $\\omega _2$ are moderate weights and $\\mascB$ is a suitable (quasi-)Banach function space, then a necessary and sufficient condition for the embedding $i\\, :\\, M (\\omega _1,\\mascB )\\to M (\\omega _2,\\mascB )$ between two modulation spaces to be compact is that the quotient $\\omega _2/\\omega _1$ vanishes at infinity. Moreover we show, that the boundedness of $\\omega _2/\\omega _1$ a necessary and sufficient condition for the previous embedding to be continuous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00948","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"}