{"paper":{"title":"Global fractional Calder\\'on-Zygmund type regularity","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelbadie Younes, Antonio J. Fern\\'andez, Boumediene Abdellaoui, Tommaso Leonori","submitted_at":"2021-07-14T08:04:29Z","abstract_excerpt":"We obtain a global fractional Calder\\'on-Zygmund regularity theory for the fractional Poisson problem. More precisely, for $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, a bounded domain with boundary $\\partial \\Omega$ of class $C^2$, $s \\in (0,1)$ and $f \\in L^m(\\Omega)$ for some $m \\geq 1$, we consider the problem $$ \\left. \\begin{aligned} (-\\Delta)^s u = f \\quad \\mbox{in } \\Omega, \\qquad\\ u = 0 \\quad \\mbox{in } \\mathbb{R}^N \\setminus \\Omega, \\end{aligned} \\right. $$ and, according to $m$, we find the values of $s \\leq t < \\min\\{1,2s\\}$ and of $1 < p < +\\infty$ such that $u \\in L^{t,p}(\\mathbb{R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06535","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/2107.06535/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"}