{"paper":{"title":"On some properties of moduli of smoothness with Jacobi weights","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":"2019-01-12T22:04:24Z","abstract_excerpt":"We discuss some properties of the moduli of smoothness with Jacobi weights that we have recently introduced and that are defined as \\[ \\omega_{k,r}^\\varphi(f^{(r)},t)_{\\alpha,\\beta,p} :=\\sup_{0\\leq h\\leq t} \\left\\| {\\mathcal{W}}_{kh}^{r/2+\\alpha,r/2+\\beta}(\\cdot) \\Delta_{h\\varphi(\\cdot)}^k (f^{(r)},\\cdot)\\right\\|_p \\] where $\\varphi(x) = \\sqrt{1-x^2}$, $\\Delta_h^k(f,x)$ is the $k$th symmetric difference of $f$ on $[-1,1]$, \\[ {\\mathcal{W}}_\\delta^{\\xi,\\zeta} (x):= (1-x-\\delta\\varphi(x)/2)^\\xi (1+x-\\delta\\varphi(x)/2)^\\zeta , \\] and $\\alpha,\\beta > -1/p$ if $0<p<\\infty$, and $\\alpha,\\beta \\geq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03907","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":""},"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"}