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As is well known, for $d=1$, the Nikolskii inequality for trigonometric polynomials on the unit circle does not have such a phenomenon."},"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":"1905.00323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-01T14:19:25Z","cross_cats_sorted":[],"title_canon_sha256":"0de2102beab5bf98d3a1131d4ea822e988b2ead94cee9aa00933886e146e1958","abstract_canon_sha256":"ffa49c03bcb44711b03841b1d4e9f2bc01af39e1387b41dc4a7ce7d75d477a14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:13.187279Z","signature_b64":"XDmfTqFVy/RUxWRyP1V01jKDDvZzGjDFNBxpf2Kp8n1+rfjmIECGkbZAhGBEhEZIJN1H9cNmgFuIb5NS35pKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8f0596aa0aa8f74240331ea421309cdc4efd30e4fef3ca14e769b96e997ea2f","last_reissued_at":"2026-05-17T23:47:13.186862Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:13.186862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nikolskii inequality for lacunary spherical polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Gorbachev, Feng Dai, Sergey Tikhonov","submitted_at":"2019-05-01T14:19:25Z","abstract_excerpt":"We prove that for $d\\ge 2$, the asymptotic order of the usual Nikolskii inequality on $\\mathbb{S}^d$ (also known as the reverse H\\\"{o}lder's inequality) can be significantly improved in many cases, for lacunary spherical polynomials of the form $f=\\sum_{j=0}^m f_{n_j}$ with $f_{n_j}$ being a spherical harmonic of degree $n_j$ and $n_{j+1}-n_j\\ge 3$. 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