{"paper":{"title":"Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amiran Gogatishvili, M\\\"ujdat A\\u{g}cayaz{\\i}, Rza Mustafayev","submitted_at":"2015-04-17T14:23:14Z","abstract_excerpt":"In this paper it is shown that the Hardy-Littlewood maximal operator $M$ is not bounded on Zygmund-Morrey space $\\mathcal{M}_{L(\\log L),\\lambda}$, but $M$ is still bounded on $\\mathcal{M}_{L(\\log L),\\lambda}$ for radially decreasing functions. The boundedness of the iterated maximal operator $M^2$ from $\\mathcal{M}_{L(\\log L),\\lambda}$ to weak Zygmund-Morrey space ${\\mathcal {W \\! M}}_{L(\\log L),\\lambda}$ is proved. The class of functions for which the maximal commutator $C_b$ is bounded from $\\mathcal{M}_{L(\\log L),\\lambda}$ to ${\\mathcal {W \\! M}}_{L(\\log L),\\lambda}$ are characterized. It i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04509","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":""},"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"}