{"paper":{"title":"Approximation by boolean sums of Jackson operators on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Feilong Cao, Yuguang Wang","submitted_at":"2014-09-13T07:39:33Z","abstract_excerpt":"This paper concerns the approximation by the Boolean sums of Jackson operators $\\oplus^rJ_{k,s}(f)$ on the unit sphere $\\mathbb S^{n-1}$ of $\\mathbb{R}^{n}$. We prove the following the direct and inverse theorem for $\\oplus^rJ_{k,s}(f)$: there are constants $C_1$ and $C_2$ such that \\begin{equation*} C_1\\|\\oplus^rJ_{k,s}f-f\\|_p \\leq \\omega^{2r}(f,k^{-1})_p \\leq C_2 \\max_{v\\geq k}\\|\\oplus^rJ_{k,s}f-f\\|_p \\end{equation*} for any positive integer $k$ and any $p$th Lebesgue integrable functions $f$ defined on $\\mathbb S^{n-1}$, where $\\omega^{2r}(f,t)_p$ is the modulus of smoothness of degree $2r$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3923","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"}