{"paper":{"title":"Schatten--Lorentz characterization of Riesz transform commutator associated with Bessel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Ji Li, Michael Lacey, Xiao Xiong, Zhijie Fan","submitted_at":"2024-03-13T05:04:05Z","abstract_excerpt":"Let $\\Delta_\\lambda$ be the Bessel operator on the upper half space $\\mathbb{R}_+^{n+1}$ with $n\\geq 0$ and $\\lambda>0$, and $R_{\\lambda,j}$ be the $j-$th Bessel Riesz transform, $j=1,\\ldots,n+1$. We demonstrate that the Schatten--Lorentz norm ($S^{p,q}$, $1<p<\\infty$, $1\\leq q\\leq \\infty$) of the commutator $[b,R_{\\lambda,j}]$ can be characterized in terms of the oscillation space norm of the symbol $b$. In particular, for the case $p=q$, the Schatten norm of $[b,R_{\\lambda,j}]$ can be further characterized in terms of the Besov norm of the symbol. Moreover, the critical index is also studied"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.08249","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/2403.08249/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"}