{"paper":{"title":"On Sharp Constants for Dual Segal--Bargmann $L^p$ Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Todd Kemp, William E. Gryc","submitted_at":"2014-01-09T00:39:54Z","abstract_excerpt":"We study dilated holomorphic $L^p$ space of Gaussian measures over $\\mathbb{C}^n$, denoted $\\mathcal{H}_{p,\\alpha}^n$ with variance scaling parameter $\\alpha>0$. The duality relations $(\\mathcal{H}_{p,\\alpha}^n)^\\ast \\cong \\mathcal{H}_{p',\\alpha}$ hold with $\\frac{1}{p}+\\frac{1}{p'}=1$, but not isometrically. We identify the sharp lower constant comparing the norms on $\\mathcal{H}_{p',\\alpha}$ and $(\\mathcal{H}_{p,\\alpha}^n)^\\ast$, and provide upper and lower bounds on the sharp upper constant. We prove several suggestive partial results on the sharpness of the upper constant. One of these par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1866","kind":"arxiv","version":2},"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"}