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Moreover, we find necessary conditions on $\\omega$ for Bernstein's inequality to hold. We also prove weighted Bernstein-Markov, Remez, and Nikolskii inequalities for trigonometric and algebraic polynomials."},"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":"1308.5818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-27T10:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"0b7b1c589cb84c929c8aa794f42c8138bf049148abaf6fb540e7494806f8728c","abstract_canon_sha256":"8c338ee1903446347afcc94135877860c96958ed03c0dff413e16036919293cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:51.102414Z","signature_b64":"g3SYxbSbBTLm5qjbbZ3Y2P/CICP+HtO9P826MIy2IU0m8anJTvk3gqm8/lOefwKJ7nHuNnf154cdgy12qQVXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"183db2ca0120c5049864b949d595ca127ec16b767952806fa87061295f93f208","last_reissued_at":"2026-05-18T03:14:51.101601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:51.101601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernstein inequalities with nondoubling weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andriy Bondarenko, Sergey Tikhonov","submitted_at":"2013-08-27T10:32:20Z","abstract_excerpt":"We answer Totik's question on weighted Bernstein's inequalities showing that $$ \\|T_n'\\|_{L_p(\\omega)} \\le C(p,\\omega)\\, {n}\\,\\|T_n\\|_{L_p(\\omega)},\\qquad 0<p\\le \\infty, $$ holds for all trigonometric polynomials $T_n$ and certain nondoubling weights $\\omega$. 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