{"paper":{"title":"One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"M. Vaughan, P. R. Stinga","submitted_at":"2018-10-31T14:35:25Z","abstract_excerpt":"We characterize one-sided weighted Sobolev spaces $W^{1,p}(\\mathbb{R},\\omega)$, where $\\omega$ is a one-sided Sawyer weight, in terms of a.e.~and weighted $L^p$ limits as $\\alpha\\to1^-$ of Marchaud fractional derivatives of order $\\alpha$. Similar results for weighted Sobolev spaces $W^{2,p}(\\mathbb{R}^n,\\nu)$, where $\\nu$ is an $A_p$-Muckenhoupt weight, are proved in terms of limits as $s\\to1^-$ of fractional Laplacians $(-\\Delta)^s$. These are Bourgain--Brezis--Mironescu-type characterizations for weighted Sobolev spaces. We also complement their work by studying a.e.~and weighted $L^p$ limi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13305","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":""},"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"}