{"paper":{"title":"A remark on the multipliers on spaces of weak products of functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Brett D. Wick, Stefan Richter","submitted_at":"2016-03-03T19:51:47Z","abstract_excerpt":"If $\\mathcal{H}$ denotes a Hilbert space of analytic functions on a region $\\Omega \\subseteq \\mathbb{C}^d$, then the weak product is defined by $$\\mathcal{H}\\odot\\mathcal{H}=\\left\\{h=\\sum_{n=1}^\\infty f_n g_n : \\sum_{n=1}^\\infty \\|f_n\\|_{\\mathcal{H}}\\|g_n\\|_{\\mathcal{H}} <\\infty\\right\\}.$$ We prove that if $\\mathcal{H}$ is a first order holomorphic Besov Hilbert space on the unit ball of $\\mathbb{C}^d$, then the multiplier algebras of $\\mathcal{H}$ and of $\\mathcal{H}\\odot\\mathcal{H}$ coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01233","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"}