{"paper":{"title":"A $p$-specific spectral multiplier theorem with sharp regularity bound for Grushin operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Lars Niedorf","submitted_at":"2021-10-19T15:35:05Z","abstract_excerpt":"In a recent work, P. Chen and E. M. Ouhabaz proved a $p$-specific $L^p$-spectral multiplier theorem for the Grushin operator acting on $\\mathbb{R}^{d_1}\\times\\mathbb{R}^{d_2}$ which is given by \\[ L =-\\sum_{j=1}^{d_1} \\partial_{x_j}^2 - \\bigg( \\sum_{j=1}^{d_1} |x_j|^2\\bigg) \\sum_{k=1}^{d_2}\\partial_{y_k}^2. \\] Their approach yields an $L^p$-spectral multiplier theorem within the range $1< p\\le \\min\\{ \\frac{2d_1}{d_1+2},\\frac{2(d_2+1)}{d_2+3} \\}$ under a regularity condition on the multiplier which is sharp only when $d_1\\ge d_2$. In this paper, we improve on this result by proving $L^p$-bounde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10058","kind":"arxiv","version":3},"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/2110.10058/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"}