{"paper":{"title":"Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jos\\'e Maria Martell (IMFF), Pascal Auscher (LM-Orsay)","submitted_at":"2006-03-28T08:06:16Z","abstract_excerpt":"This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular 'non-integral' operators arising from $L$ ; those are the operators $\\phi(L)$ for bounded holomorphic functions $\\phi$, the Riesz transforms $\\nabla L^{-1/2}$ (or $(-\\Delta)^{1/2}L^{-1/2}$) and its inverse $L^{1/2}(-\\Delta)^{-1/2}$, some quadratic functionals $g\\_{L}$ and $G\\_{L}$ of Littlewood-Paley-Stein type and also some vector-valued inequalities such as the ones"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603642","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"}