{"paper":{"title":"Potential maps, Hardy spaces, and tent spaces on special Lipschitz domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Alan McIntosh, Martin Costabel, Robert J. Taggart","submitted_at":"2010-06-03T07:02:33Z","abstract_excerpt":"Suppose that $\\Omega$ is the open region in $\\mathbb{R}^n$ above a Lipschitz graph and let $d$ denote the exterior derivative on $\\mathbb{R}^n$. We construct a convolution operator $T $ which preserves support in $\\bar{\\Omega$}, is smoothing of order 1 on the homogeneous function spaces, and is a potential map in the sense that $dT$ is the identity on spaces of exact forms with support in $\\bar\\Omega$. Thus if $f$ is exact and supported in $\\bar\\Omega$, then there is a potential $u$, given by $u=Tf$, of optimal regularity and supported in $\\bar\\Omega$, such that $du=f$. This has implications f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0562","kind":"arxiv","version":2},"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"}