{"paper":{"title":"Sobolev improving for averages over curves in $\\mathbf{R^4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, David Beltran, Jonathan Hickman, Shaoming Guo","submitted_at":"2021-02-17T15:08:27Z","abstract_excerpt":"We study $L^p$-Sobolev improving for averaging operators $A_{\\gamma}$ given by convolution with a compactly supported smooth density $\\mu_{\\gamma}$ on a non-degenerate curve. In particular, in 4 dimensions we show that $A_{\\gamma}$ maps $L^p(\\mathbb{R}^4)$ the Sobolev space $L^p_{1/p}(\\mathbb{R}^4)$ for all $6 < p < \\infty$. This implies the complete optimal range of $L^p$-Sobolev estimates, except possibly for certain endpoint cases. The proof relies on decoupling inequalities for a family of cones which decompose the wave front set of $\\mu_{\\gamma}$. In higher dimensions, a new non-trivial n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.08806","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/2102.08806/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"}