{"paper":{"title":"Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy--Landau--Littlewood inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Egor D. Kosov, Georgii I. Zelenov, Vladimir I. Bogachev","submitted_at":"2016-02-16T21:17:51Z","abstract_excerpt":"We prove that the distribution density of any non-constant polynomial $f(\\xi_1,\\xi_2,\\ldots)$ of degree $d$ in independent standard Gaussian random variables $\\xi$ (possibly, in infinitely many variables) always belongs to the Nikol'skii--Besov space $B^{1/d}(\\mathbb{R}^1)$ of fractional order $1/d$ (and this order is best possible), and an analogous result holds for polynomial mappings with values in $\\mathbb{R}^k$.\n  Our second main result is an upper bound on the total variation distance between two probability measures on $\\mathbb{R}^k$ via the Kantorovich distance between them and a suita"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05207","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"}