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We prove the weighted boundedness of $B\\mathcal{I}_\\alpha$ on the Morrey type spaces. Moreover, an Olsen type inequality for $B\\mathcal{I}_\\alpha$ is also given."},"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":"1808.05189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-15T17:17:31Z","cross_cats_sorted":[],"title_canon_sha256":"e4245f5df7b9154259ed206fdc63bb4ea3dc8bb167b8beeae88c42117873746b","abstract_canon_sha256":"d7a28f68321077b38419c0470f01175a76b75ec903d6dcfb4dabca442a7919f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:01.370240Z","signature_b64":"oww4uQqwUs9sfPAlPvybldCDWpx3yKr6dNNPy2KvLq5a545sfXJ7OevtWdfqCvnefiCIZR+HRwE9gEQP8bqzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3717725cfd21ab4037fde23fd0ba6ec180d9a9bb80ab057874a3ec6c2925d108","last_reissued_at":"2026-05-18T00:08:01.369689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:01.369689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some estimates for the bilinear fractional integrals on the Morrey space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Huihui Zhang, Jianmiao Ruan, Xiangxing Tao, Xiao Yu","submitted_at":"2018-08-15T17:17:31Z","abstract_excerpt":"In this paper, we are interested in the following bilinear fractional integral operator $B\\mathcal{I}_\\alpha$ defined by\n  \\[ B\\mathcal{I}_{\\alpha}({f,g})(x)=\\int_{% %TCIMACRO{\\U{211d} }% %BeginExpansion \\mathbb{R} %EndExpansion ^{n}}\\frac{f(x-y)g(x+y)}{|y|^{n-\\alpha}}dy, \\] with $0< \\alpha<n$. We prove the weighted boundedness of $B\\mathcal{I}_\\alpha$ on the Morrey type spaces. 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