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Let $\\triangle$ be the closed triangle with vertices $P=(\\frac{2}{5}, \\frac{1}{5}), ~ Q=(\\frac{1}{2}, \\frac{1}{2}), ~ R=(0, 0).$\n  In this paper, we prove that for $ (\\frac{1}{p}, \\frac{1}{q}) \\in \\left[(\\f"},"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":"1609.08140","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-26T19:53:46Z","cross_cats_sorted":[],"title_canon_sha256":"85991cfa21672df4a8e9f7148df78192dec92b508293c1baa08ff03c64e82f68","abstract_canon_sha256":"6955ac5c703d0ee5765d42a3edd2ffefbe3a7471f28e9bd3886977137510a22e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:27.726073Z","signature_b64":"Xv74VwWwrlTs0BKovCLIHmyNi6otzE0Iw0v+jbqYmenBuJnoKt8QaNXIYWrrEugsVsXvYXnbyW0duhyBoIV3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04ee534f1ddeb7656248b261dd95261bd62a7562dbcbcbf01069d2f11754b553","last_reissued_at":"2026-05-18T00:20:27.725527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:27.725527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal functions associated to flat plane curves with Mitigating factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ramesh Manna","submitted_at":"2016-09-26T19:53:46Z","abstract_excerpt":"We study the boundedness problem for maximal operators $\\mathbb{M}_{\\sigma}$ associated to flat plane curves with Mitigating factors, defined by $$\\mathbb{M}_{\\sigma}f(x) \\, := \\, \\sup_{1 \\leq t \\leq 2} \\left|\\int_{0}^{1} f(x-t\\Gamma(s)) \\, (\\kappa(s))^{\\sigma} \\, ds\\right|,$$ where $\\kappa(s)$ denotes the curvature of the curve $\\Gamma(s)=(s, g(s)+1), ~g(s) \\in C^5[0,1]$ in $\\mathbb{R}^2$. 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