{"paper":{"title":"H\\\"older continuity of Tauberian constants associated with discrete and ergodic strong maximal operators","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":"2016-12-02T20:17:46Z","abstract_excerpt":"This paper concerns the smoothness of Tauberian constants of maximal operators in the discrete and ergodic settings. In particular, we define the discrete strong maximal operator $\\tilde{M}_S$ on $\\mathbb{Z}^n$ by \\[\n  \\tilde{M}_S f(m) := \\sup_{0 \\in R \\subset \\mathbb{R}^n}\\frac{1}{\\#(R \\cap \\mathbb{Z}^n)}\\sum_{ j\\in R \\cap \\mathbb{Z}^n} |f(m+j)|,\\qquad m\\in \\mathbb{Z}^n, \\] where the supremum is taken over all open rectangles in $\\mathbb{R}^n$ containing the origin whose sides are parallel to the coordinate axes. We show that the associated Tauberian constant $\\tilde{C}_S(\\alpha)$, defined by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00822","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"}