{"paper":{"title":"On the $L^p$-estimates of Riesz transforms on forms over complete Riemanian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiang-Dong Li","submitted_at":"2013-04-10T21:34:57Z","abstract_excerpt":"In our previous paper \\cite{Li2010}, we proved a martingale transform representation formula for the Riesz transforms on forms over complete Riemannian manifolds, and proved some explicit $L^p$-norm estimates for the Riesz transforms on complete Riemannian manifolds with suitable curvature conditions. In this paper we correct a gap contained in \\cite{Li2010} and prove that the main result obtained in \\cite{Li2010} on the $L^p$-norm estimates for the Riesz transforms on forms remain valid. Moreover, we prove a time reversal martingale transform representation formula for the Riesz transforms on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3150","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":""},"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"}