{"paper":{"title":"Solyanik estimates in ergodic theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein","submitted_at":"2015-03-10T13:45:45Z","abstract_excerpt":"Let $U_1, \\ldots, U_n$ be a collection of commuting measure preserving transformations on a probability space $(\\Omega, \\Sigma, \\mu)$. Associated with these measure preserving transformations is the ergodic strong maximal operator $\\mathsf M ^\\ast _{\\mathsf S}$ given by \\[ \\mathsf M ^\\ast _{\\mathsf S} f(\\omega) := \\sup_{0 \\in R \\subset \\mathbb{R}^n}\\frac{1}{\\#(R \\cap \\mathbb{Z}^n)}\\sum_{(j_1, \\ldots, j_n) \\in R\\cap \\mathbb{Z}^n}\\big|f(U_1^{j_1}\\cdots U_n^{j_n}\\omega)\\big|, \\] where the supremum is taken over all open rectangles in $\\mathbb{R}^n$ containing the origin whose sides are parallel t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02900","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":""},"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"}