{"paper":{"title":"Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javanshir J. Hasanov, Vagif S. Guliyev, Xayyam A. Badalov","submitted_at":"2018-12-18T11:52:52Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^n$ be an unbounded open set. We consider the generalized weighted Morrey spaces $\\mathcal{M}^{p(\\cdot),\\varphi}_{\\omega}(\\Omega)$ and the vanishing generalized weighted Morrey spaces $V\\mathcal{M}^{p(\\cdot),\\varphi}_{\\omega}(\\Omega)$ with variable exponent $p(x)$ and a general function $\\varphi(x,r)$ defining the Morrey-type norm. The main result of this paper are the boundedness of Riesz potential and its commutators on the spaces $\\mathcal{M}^{p(\\cdot),\\varphi}_{\\omega}(\\Omega)$ and $V\\mathcal{M}^{p(\\cdot),\\varphi}_{\\omega}(\\Omega)$. This result generalizes sev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07314","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":""},"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"}