{"paper":{"title":"Calderon-type commutators and chamber lifting in the Dunkl setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Eric Sawyer, Ji Li, Liangchuan Wu, Ming-Yi Lee, Yongsheng Han","submitted_at":"2026-05-25T13:01:43Z","abstract_excerpt":"We study Calder\\'on-type commutators $[M_b,T_i\\mathcal R_j]$ in the rational Dunkl setting with a finite reflection group $G$. If $b$ belongs to the orbit Lipschitz class $\\operatorname{Lip}_d$, then for every $1<p<\\infty$ we prove $$\\|[M_b,T_i\\mathcal R_j]f\\|_{L^p(\\mathbb{R}^N,d\\omega)}\\le C_p\\|b\\|_{\\operatorname{Lip}_d}\\|f\\|_{L^p(\\mathbb{R}^N,d\\omega)}.$$ No $G$-invariance is imposed on the input function $f$.\n  The key is a chamber lifting: fix a closed Weyl chamber $\\mathcal C$ and set $Uf(x)=(f(\\sigma_1x),\\dots,f(\\sigma_{|G|}x))$ for $x\\in\\mathcal C$. This identifies $L^p(\\mathbb{R}^N,d\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25808","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/2605.25808/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"}