{"paper":{"title":"Solutions of the divergence equation in Hardy and lipschitz spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Mar\\'ia Eugenia Cejas, Ricardo G. Dur\\'an","submitted_at":"2024-12-30T16:07:55Z","abstract_excerpt":"Given a bounded domain $\\O$ and $f$ of zero integral, the existence of a vector fields $\\u$ vanishing on $\\partial\\O$ and satisfying $\\d\\u=f$ has been widely studied because of its connection with many important problems. It is known that for $f\\in L^p(\\O)$, $1<p<\\infty$, there exists a solution $\\u\\in W^{1,p}_0(\\O)$, and also that an analogous result is not true for $p=1$ or $p=\\infty$. The goal of this paper is to prove results for Hardy spaces when $\\frac{n}{n+1}<p\\le 1$, and in the other limiting case, for bounded mean oscillation and Lipschitz spaces. As a byproduct of our analysis we obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21048","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.21048/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}