{"paper":{"title":"Annulus Maximal Averages on Variable Hyperplanes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joonil Kim","submitted_at":"2019-06-10T05:10:43Z","abstract_excerpt":"By giving a thin width of $0<\\delta\\ll 1$ to both a unit circle and a unit line, we set an annulus and a tube on the Euclidean plane $\\mathbb{R}^2$. Consider the maximal means $M_\\delta$ over dilations of the annulus, and $N_\\delta$ over rotations of the tube. It is known that their operator norms on $L^2(\\mathbb{R}^2)$ are $O(|\\log 1/\\delta|^{1/2})$. In this paper, we study the maximal averages $\\mathcal{M}^A_\\delta$ and $\\mathcal{N}^A_\\delta$ over those annuli and tubes now imbedded on the variable hyperplanes $(x,x_3)+\\left\\{\\left(y, \\langle A(x), y\\rangle\\right): y\\in\\mathbb{R}^2\\right\\}\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03797","kind":"arxiv","version":2},"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/1906.03797/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"}