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We apply these to prove the embedding $H^p_D(\\wedge T^*M) \\subseteq L^p(\\wedge T^*M)$, $1\\leq p\\leq 2$, for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ, where $D=d+d^*$ is the Hodge--Dirac oper"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.0168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-31T08:58:04Z","cross_cats_sorted":["math.AP","math.DG","math.FA"],"title_canon_sha256":"7bec64bfefff4fa3baf39bbd84718307530aa7665ab46d24e0cb354daf9333bb","abstract_canon_sha256":"a60326dc258d3a292fc5b7f183676b6d4a293b2ca8fd022368f9ea02160a91ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:25.837444Z","signature_b64":"q7y/0gncx2/NAZpzv+KLWYbTTn57GHGqtNm26BYKCB7YZh4RIJtXfMImdLFpJTUTjCWvrAxYSOqaVUxe+fgLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bbb3dcb229fd2012c4f02e6945be37966cba0fe2870bf4336276316fd7e5412","last_reissued_at":"2026-05-18T03:29:25.836729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:25.836729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calderon Reproducing Formulas and Applications to Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.FA"],"primary_cat":"math.CA","authors_text":"Alan Mcintosh (CMA), Andrew Morris (MI), Pascal Auscher (LM-Orsay)","submitted_at":"2013-03-31T08:58:04Z","abstract_excerpt":"We establish new Calder\\'{o}n reproducing formulas for self-adjoint operators $D$ that generate strongly continuous groups with finite propagation speed. 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