{"paper":{"title":"H-distribution via Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ivana Vojnovic, Jelena Aleksic, Stevan Pilipovic","submitted_at":"2016-09-19T12:08:24Z","abstract_excerpt":"H-distributions associated to weakly convergent sequences in Sobolev spaces are determined. It is shown that a weakly convergent sequence $(u_n)$ in $W^{-k,p}( \\R^d)$ has the property that $\\theta u_n$ converges strongly in $W^{-k,p}(\\R^d)$ for every $\\theta\\in\\mathcal S(\\R^d)$ if and only if all H-distributions related to this sequence are equal to zero. Results are applied on a weakly convergent sequence of solutions to a family of linear first order PDEs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05681","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"}