{"paper":{"title":"Embedding Bergman spaces into tent spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a, Kian Sierra","submitted_at":"2015-04-13T08:08:47Z","abstract_excerpt":"Let $A^p_\\omega$ denote the Bergman space in the unit disc $\\mathbb{D}$ of the complex plane induced by a radial weight $\\omega$ with the doubling property $\\int_{r}^1\\omega(s)\\,ds\\le C\\int_{\\frac{1+r}{2}}^1\\omega(s)\\,ds$. The tent space $T^q_s(\\nu,\\omega)$ consists of functions such that\n  \\begin{equation*}\n  \\begin{split}\n  \\|f\\|_{T^q_s(\\nu,\\omega)}^q\n  =\\int_{\\mathbb{D}}\\left(\\int_{\\Gamma(\\zeta)}|f(z)|^s\\,d\\nu(z)\\right)^\\frac{q}s\\omega(\\zeta)\\,dA(\\zeta)\n  <\\infty,\\quad 0<q,s<\\infty.\n  \\end{split}\n  \\end{equation*} Here $\\Gamma(\\zeta)$ is a non-tangential approach region with vertex $\\zeta$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03091","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"}