{"paper":{"title":"Conservation de certaines propri\\'et\\'es \\`a travers un contr\\^ole \\'epars d'un op\\'erateur et applications au projecteur de Leray-Hopf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cristina Benea, Fr\\'ed\\'eric Bernicot","submitted_at":"2017-03-01T10:59:51Z","abstract_excerpt":"Nous poursuivons l'\\'etude d'un contr\\^ole \\'epars d'un op\\'erateur singulier. Plus pr\\'ecis\\'ement nous expliquons comment on peut conserver certaines propri\\'et\\'es de l'op\\'erateur initial \\`a travers un tel contr\\^ole et d\\'ecrivons quelques applications: bornitude de l'adjoint de la transform\\'ee de Riesz et du projecteur de Leray. De plus, nous nous int\\'eresserons \\`a donner un regard nouveau sur les dominations \\'eparses \\`a travers les oscillations et les fonctions carr\\'ees localis\\'ees. Aussi, nous d\\'evoilerons une connexion entre les bons intervalles de la d\\'ecomposition \\'eparse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00228","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"}