{"paper":{"title":"The existence and boundedness of multilinear Marcinkiewicz integrals on Companato spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kozo Yabuta, Qingying Xue","submitted_at":"2015-12-02T12:12:08Z","abstract_excerpt":"In this paper, we established the boundedness of m-linear Marcinkiewicz integral on Campanato type spaces. We showed that if the $m$-linear Marcinkiewicz integral is finite for one point, then it is finite almost everywhere. Moreover, the following norm inequality holds, $$\\|\\mu(\\vec{f})\\|_{\\mathcal{E}^{\\alpha,p}} \\leq C\\prod_{j=1}^m\\|f_j\\|_{\\mathcal{E}^{\\alpha_j,p_j}},$$ where $\\mathcal{E}^{\\alpha,p}$ is the classical Campanato spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00663","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"}