{"paper":{"title":"Littlewood-Paley formulas and Carleson measures for weighted Fock spaces induced by $A_\\infty$-type weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Carme Cascante, Joan F\\`abrega, Jos\\'e A. Pel\\'aez","submitted_at":"2016-12-22T06:32:03Z","abstract_excerpt":"We obtain Littlewood-Paley formulas for Fock spaces $\\mathcal{F}^q_{\\beta,\\omega}$ induced by weights $\\omega\\in A^{restricted}_\\infty=\\cup_{1\\le p<\\infty}A^{restricted}_{p}$, where $A^{restricted}_{p}$ is the class of weights such that the Bergman projection $P_\\alpha$, on the classical Fock space $\\mathcal{F}^2_{\\alpha}$, is bounded on\n  $$\\mathcal{L}^p_{\\alpha,\\omega}:=\\left\\{f:\\, \\int_{\\mathbb{C}}|f(z)|^pe^{-p\\frac{\\alpha}{2}|z|^2}\\,\\omega(z)dA(z)<\\infty \\right\\}. $$\n  Using these equivalent norms for $\\mathcal{F}^q_{\\beta,\\omega}$ we characterize the Carleson measures for weighted Fock-So"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07458","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"}