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We prove that if the coefficients a_{ij} are H\\\"older continuous with respect to the distance induced by the vector fields, then local Schauder estimates on X_{i}X_{j}u, X_{0}u hold; if the coefficients belong"},"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":"1103.5116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-26T08:26:13Z","cross_cats_sorted":[],"title_canon_sha256":"d16cfad99cddddca0b2112579add22f9e8a0e902110b7a2d2c5bbbb6180a907b","abstract_canon_sha256":"fb8c65d295e2dd3775c07d0d2e5ef511813121efe39ae2c54573b4c15cd70dee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:29.045289Z","signature_b64":"yLEKcMd+75XVunrccT0OcBBdndbCxNDDDNkwKRwSwhyw2SAhok19D2MeIQudjpAFc6M6vrqb1yUR4AiH212qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3430850293a8f347d8b350783f3afb887d6d0a0f6580d42b834490291fa73c38","last_reissued_at":"2026-05-18T01:22:29.044648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:29.044648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L^p and Schauder estimates for nonvariational operators structured on H\\\"ormander vector fields with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Maochun Zhu, Marco Bramanti","submitted_at":"2011-03-26T08:26:13Z","abstract_excerpt":"We consider linear second order nonvariational partial differential operators of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the X_{i}'s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfying H\\\"ormander's condition and a_{ij} (i,j=1,2,...,q) are real valued, bounded measurable functions, such that the matrix {a_{ij}} is symmetric and uniformly positive. 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