{"paper":{"title":"Multiversion of the Hausdorff--Young inequality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.CV","math.PR"],"primary_cat":"math.FA","authors_text":"Paata Ivanisvili, Pavlos Kalantzopoulos","submitted_at":"2025-06-10T06:41:31Z","abstract_excerpt":"We consider a family of jointly Gaussian random vectors $\\xi_j \\in \\mathbb{R}^{k_j}$, each standard normal but possibly correlated, and investigate when\\[ \\mathbb{E}\\, F\\!\\Bigl(B\\bigl(|T_{z_1} f_1(\\xi_1)|,\\dots,|T_{z_n} f_n(\\xi_n)|\\bigr)\\Bigr) \\;\\;\\le\\;\\; F\\!\\Bigl(\\,\\mathbb{E}\\,B\\bigl(|f_1(\\xi_1)|,\\dots,|f_n(\\xi_n)|\\bigr)\\Bigr) \\] holds, where $T_{z}$ is either a Mehler transform $(z \\in \\mathbb{C})$ or a noise operator $(z \\in \\mathbb{R})$. This framework unifies and extends real and complex hypercontractivity to multi-function settings, yielding multiversions of the sharp Hausdorff--Young in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08494","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08494/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}