{"paper":{"title":"$L^p$-improving bounds for spherical maximal operators over restricted dilation sets: radial improvement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Shuijiang Zhao","submitted_at":"2024-12-13T05:51:47Z","abstract_excerpt":"In this paper, we study the spherical maximal operator $ M_E $ over $ E\\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two dimensions, sharp results are also obtained for quasi-Assouad regular sets $E$. A notable feature is that the high-dimensional results depend solely on the upper Minkowski dimension, while the two-dimensional results also involve other concepts in fractal geometry such as the Assouad spectrum. Additionally, the geometric shapes of the regions corresponding to the sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.09882","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/2412.09882/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"}