{"paper":{"title":"Dimension-free bounds for {R}iesz transforms on the {H}amming cube via a {B}ellman function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Alexander Volberg, Komla Domelevo, Paata Ivanisvili, Stefanie Petermichl","submitted_at":"2026-06-18T14:30:49Z","abstract_excerpt":"We give a Bellman-function proof of the dimension-free estimate \\[ \\Big\\| \\vec{R} f \\Big\\|_{L^p(\\Omega;\\,\\ell^2)} \\lesssim (p-1) \\,\\|f\\|_{L^p(\\Omega)}, \\qquad 2\\le p<\\infty, \\] for the vector of Riesz transforms associated with the Walsh number operator on the Hamming cube $\\Omega=\\{-1,1\\}^n$, as well as for locally compact abelian groups, in particular $\\Omega=\\mathbb{Z}^n$. The argument is based on a Poisson semigroup representation, symmetrized estimates along edges of $\\Omega$, and a two-point inequality. This is the first non noncommutative proof of this result, after the seminal papers o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20289","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/2606.20289/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"}