{"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. Moreover, an Olsen type inequality for $B\\mathcal{I}_\\alpha$ is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05189","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"}