{"paper":{"title":"Partial spectral multipliers and partial Riesz transforms for degenerate operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. F. M. ter Elst, E. M. Ouhabaz","submitted_at":"2012-02-09T21:39:44Z","abstract_excerpt":"We consider degenerate differential operators $A = \\displaystyle{\\sum_{k,j=1}^d \\partial_k (a_{kj} \\partial_j)}$ on $L^2(\\mathbb{R}^d)$ with real symmetric bounded measurable coefficients. Given a function $\\chi \\in C_b^\\infty(\\mathbb{R}^d)$ (respectively, $\\Omega$ a bounded Lipschitz domain) and suppose that $(a_{kj}) \\ge \\mu > 0$ a.e.\\ on $ \\supp \\chi$ (resp., a.e.\\ on $\\Omega$). We prove a spectral multiplier type result: if $F\\colon [0, \\infty) \\to \\mathbb{C}$ is such that $\\sup_{t > 0} \\| \\varphi(.) F(t .) \\|_{C^s} < \\infty$ for some non-trivial function $\\varphi \\in C_c^\\infty(0,\\infty)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2136","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"}