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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.00822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-02T20:17:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"80d8c939b3ac3accf37dc0fb2486a287a635c4b876f4ec25a92f344cd60d5481","abstract_canon_sha256":"9f8c43f40593813be8ac6e6af426f502a92a0069557b87b971c9e72a5728546d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:27.086506Z","signature_b64":"D+h3p8mxmDWk1uFk5UhNcjnP6pcK/q2oU4mezpBD3d/VzyEf32n8WImLBfSSmj51XqQjcXnLq/f/hXyzSH/UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee9ce2e98fa642e5ac0045647181f8315677ced6dbd48c6a9f2d4638b2687bd5","last_reissued_at":"2026-05-18T00:25:27.085847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:27.085847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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