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Hagelstein","submitted_at":"2013-10-14T18:31:39Z","abstract_excerpt":"Let $\\mathcal{B}$ denote a collection of open bounded sets in $\\mathbb{R}^n$, and define the associated maximal operator $M_{\\mathcal{B}}$ by $$ M_{\\mathcal{B}}f(x) := \\sup_{x \\in R \\in \\mathcal{B}} \\frac{1}{|R|}\\int_R |f|. $$ The sharp Tauberian constant of $M_{\\mathcal{B}}$ associated to $\\alpha$, denoted by $C_{\\mathcal{B}}(\\alpha)$, is defined as $$ C_{\\mathcal{B}}(\\alpha) := \\sup_{E :\\, 0 < |E| < \\infty}\\frac{1}{|E|}\\big|\\big\\{x \\in \\mathbb{R}^n:\\, M_{\\mathcal{B}}\\chi_E (x) > \\alpha\\big\\}\\big|.$$ Motivated by previous work of A. A. Solyanik, we show that if $M_{\\mathcal{B}}$ is the uncent"},"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":"1310.3771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-14T18:31:39Z","cross_cats_sorted":[],"title_canon_sha256":"d82a7f63c1543559ff5429e894bba62cba07fc239de09310aa8e2bdb95c87497","abstract_canon_sha256":"382d27ab27809394077ae6c49c9cde8b283a8dedaa466f7337fd0441cfa498f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:35.919213Z","signature_b64":"falgJuGL+7zm85fcQ6RZZq3Dp0cD8jVFtsx+K/xeGH4LuWHj6rMylUBZqyhsBVlZ4GTjWljvcCmU3MgTS3TpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a482394f1a1e9a5f9966eb09ac1d96c5f16ef65121fe34b8e9583d786d971ec1","last_reissued_at":"2026-05-18T01:34:35.918704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:35.918704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solyanik estimates in harmonic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein","submitted_at":"2013-10-14T18:31:39Z","abstract_excerpt":"Let $\\mathcal{B}$ denote a collection of open bounded sets in $\\mathbb{R}^n$, and define the associated maximal operator $M_{\\mathcal{B}}$ by $$ M_{\\mathcal{B}}f(x) := \\sup_{x \\in R \\in \\mathcal{B}} \\frac{1}{|R|}\\int_R |f|. $$ The sharp Tauberian constant of $M_{\\mathcal{B}}$ associated to $\\alpha$, denoted by $C_{\\mathcal{B}}(\\alpha)$, is defined as $$ C_{\\mathcal{B}}(\\alpha) := \\sup_{E :\\, 0 < |E| < \\infty}\\frac{1}{|E|}\\big|\\big\\{x \\in \\mathbb{R}^n:\\, M_{\\mathcal{B}}\\chi_E (x) > \\alpha\\big\\}\\big|.$$ Motivated by previous work of A. A. 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