{"paper":{"title":"On Sharp Estimates of Derivatives of Even Order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"I.A.Sheipak, T.A.Garmanova","submitted_at":"2026-06-21T19:12:14Z","abstract_excerpt":"The norms of embedding operators of Sobolev spaces $\\Wo^n_2[0;1]\\hookrightarrow\\Wo^k_\\infty[0;1]$ ($0\\leqslant k\\leqslant n-1$) are considered.\n  The least possible quantities $A^2_{n,k}(x)$ in the inequalities $|f^{(k)}(x)|^2\\leqslant A^2_{n,k}(x)\\|f^{(n)}\\|^2_{L_2[0;1]}$ are studied.\n  On the basis of the relations between the $A^2_{n,k}(x)$ and the antiderivatives of the Legendre polynomials, the properties of the maxima of the functions $A^2_{n,k}(x)$ are established.\n  It is shown that, for all~$k$, the global maximum of the function $A^2_{n,k}$ on the closed interval $[0;1]$ is the maxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22646","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22646/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}