{"paper":{"title":"Local Hardy Spaces of Differential Forms on Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alan McIntosh, Andrea Carbonaro, Andrew J. Morris","submitted_at":"2010-03-31T22:05:16Z","abstract_excerpt":"We define local Hardy spaces of differential forms $h^p_{\\mathcal D}(\\wedge T^*M)$ for all $p\\in[1,\\infty]$ that are adapted to a class of first order differential operators $\\mathcal D$ on a complete Riemannian manifold $M$ with at most exponential volume growth. In particular, if $D$ is the Hodge--Dirac operator on $M$ and $\\Delta=D^2$ is the Hodge--Laplacian, then the local geometric Riesz transform ${D(\\Delta+aI)^{-{1}/{2}}}$ has a bounded extension to $h^p_D$ for all $p\\in[1,\\infty]$, provided that $a>0$ is large enough compared to the exponential growth of $M$. A characterisation of $h^1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0018","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"}