{"paper":{"title":"Schur multipliers on $\\mathcal{B}(L^p,L^q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cl\\'ement Coine","submitted_at":"2017-03-23T16:17:27Z","abstract_excerpt":"Let $(\\Omega_1, \\mathcal{F}_1, \\mu_1)$ and $(\\Omega_2, \\mathcal{F}_2, \\mu_2)$ be two measure spaces and let $1 \\leq p,q \\leq +\\infty$. We give a definition of Schur multipliers on $\\mathcal{B}(L^p(\\Omega_1), L^q(\\Omega_2))$ which extends the definition of classical Schur multipliers on $\\mathcal{B}(\\ell_p,\\ell_q)$. Our main result is a characterization of Schur multipliers in the case $1\\leq q \\leq p \\leq +\\infty$. When $1 < q \\leq p < +\\infty$, $\\phi \\in L^{\\infty}(\\Omega_1 \\times \\Omega_2)$ is a Schur multiplier on $\\mathcal{B}(L^p(\\Omega_1), L^q(\\Omega_2))$ if and only if there are a measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08128","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"}