{"paper":{"title":"Maximal, potential and singular operators in the local \"complementary\" variable exponent Morrey type spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javanshir J. Hasanov, Stefan G. Samko, Vagif S. Guliyev","submitted_at":"2011-09-26T13:46:14Z","abstract_excerpt":"We consider local \"complementary\" generalized Morrey spaces ${\\dual \\cal M}_{\\{x_0\\}}^{p(\\cdot),\\om}(\\Om)$ in which the $p$-means of function are controlled over $\\Om\\backslash B(x_0,r)$ instead of $B(x_0,r)$, where $\\Om \\subset \\Rn$ is a bounded open set, $p(x)$ is a variable exponent, and no monotonicity type conditio is imposed onto the function $\\om(r)$ defining the \"complementary\" Morrey-type norm. In the case where $\\om$ is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5565","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"}