{"paper":{"title":"Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $\\mathbb Z^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Elias M. Stein, Jean Bourgain, Mariusz Mirek","submitted_at":"2018-04-20T15:34:33Z","abstract_excerpt":"Dimension-free bounds will be provided in maximal and $r$-variational inequalities on $\\ell^p(\\mathbb Z^d)$ corresponding to the discrete Hardy-Littlewood averaging operators defined over the cubes in $\\mathbb Z^d$. We will also construct an example of a symmetric convex body in $\\mathbb Z^d$ for which maximal dimension-free bounds fail on $\\ell^p(\\mathbb Z^d)$ for all $p\\in(1, \\infty)$. Finally, some applications in ergodic theory will be discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07679","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"}