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Let $\\mathcal{M}_{\\mathcal{R}}^{\\vec{\\Psi}}$ be the multilinear strong maximal function with Orlicz norms which is defined by $$\\mathcal{M}_{\\mathcal{R}}^{\\vec{\\Psi}}(\\vec{f})(x)=\\sup_{R\\in \\mathcal{R},R\\ni x}\\prod^{m}_{j=1}\\|f_{j}\\|_{\\Psi_{j},R}$$ where the supremum is taken over all rectangles with sides parallel to the coordinate axes. If $\\Psi_j(t)=t$, then $\\mathcal{M}_{\\mathcal{R}}^{\\vec{t}}$ coincides with the multilinear strong mximal function $\\mathcal{M}"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.00155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-01T13:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"773bcc28a6bb4d855f90e78b5a3f0a6cd281dce5b1ad1852239e46deae6781fc","abstract_canon_sha256":"fd8c39ab2c254accf1c619adc20ccf9bcfbf9088c660e9aeea810c71ace8b784"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:04.294650Z","signature_b64":"tuaXSw1x1RdrM9pRWPIRcFfHDS3Mw2kLS/8UcX4MsirBZW4yunUW5RYWnetDv8EsqEP2JMP/Y11f44t+ZSy1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39582d2e600cb8606a4ba5e1b4c7634749aa5d4ca1eadc51a1cd0ad10dfd38a2","last_reissued_at":"2026-05-18T00:41:04.293906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:04.293906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fefferman-Stein type inequalities for the multilinear strong maximal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hiroki Saito, Juan Zhang, Qingying Xue","submitted_at":"2017-07-01T13:21:07Z","abstract_excerpt":"Let $\\vec{\\omega}=( \\omega_{1},...,\\omega_{m})$ be a multiple weight and $\\{\\Psi_{j}\\}^{m}_{j=1}$ be a sequence of Young functions. 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