{"paper":{"title":"New moduli of smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. Leviatan, I. A. Shevchuk, K. A. Kopotun","submitted_at":"2014-08-09T04:09:59Z","abstract_excerpt":"In this paper, we discuss various properties of the new modulus of smoothness \\[ \\omega^\\varphi_{k,r}(f^{(r)},t)_p := \\sup_{0 < h\\leq t}\\|\\mathcal W^r_{kh}(\\cdot) \\Delta_{h\\varphi(\\cdot)}^k (f^{(r)},\\cdot)\\|_{L_p[-1,1]}, \\] where $\\mathcal W_\\delta(x) = \\bigl((1-x-\\delta\\varphi(x)/2) (1+x-\\delta\\varphi(x)/2)\\bigr)^{1/2}. $\n  Related moduli with more general weights are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2018","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}