{"paper":{"title":"Bilinear Forms on the Dirichlet Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Brett D. Wick, Eric Sawyer, Nicola Arcozzi, Richard Rochberg","submitted_at":"2008-11-25T15:14:32Z","abstract_excerpt":"Let $\\mathcal{D}$ be the classical Dirichlet space, the Hilbert space of holomorphic functions on the disk. Given a holomorphic symbol function $b$ we define the associated Hankel type bilinear form, initially for polynomials f and g, by $T_{b}(f,g):= < fg,b >_{\\mathcal{D}} $, where we are looking at the inner product in the space $\\mathcal{D}$.\n  We let the norm of $T_{b}$ denotes its norm as a bilinear map from $\\mathcal{D}\\times\\mathcal{D}$ to the complex numbers. We say a function $b$ is in the space $\\mathcal{X}$ if the measure $d\\mu_{b}:=| b^{\\prime}(z)| ^{2}dA$ is a Carleson measure for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4107","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"}