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When $q=\\infty$ we obtain boundedness for $T_\\Omega$ from $L^{p_1}(\\mathbb R^n)\\times L^{p_2}(\\mathbb R^n)$ to $ L^p(\\mathbb R^n) $ when $1<p_1, p_2<\\infty$ and $1/p=1/p_1+1/p_2$. For $q=2$ we obtain that $T_\\Omega$ is bounded from $L^{2}(\\mathbb R^n)\\times L^{ 2}(\\mathbb R^n)$ to $ ","authors_text":"Danqing He, Loukas Grafakos, Petr Honz\\'ik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-21T03:03:38Z","title":"Rough Bilinear Singular Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06099","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:74c0bbb0b5a40848194a8c45ac0e32de022c01c86eac62656b678f113e6559df","target":"record","created_at":"2026-05-18T01:32:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8c9d94450ef7bdbc7e1deb9d7fb4ddf9ab1b606308ea241a3af8cd1bbf260ca0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-21T03:03:38Z","title_canon_sha256":"f0182be347182be8ee75796a6b7ba13e810d4c49b3095902de324573752e4e3b"},"schema_version":"1.0","source":{"id":"1509.06099","kind":"arxiv","version":2}},"canonical_sha256":"36e6f345b6a3bc18de1d2fbd37dacb1890fbf91a8952c336cded0383adf6b468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36e6f345b6a3bc18de1d2fbd37dacb1890fbf91a8952c336cded0383adf6b468","first_computed_at":"2026-05-18T01:32:20.551386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:20.551386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BgI0RujLBOJlb7XsrF9quoIReVQEwjNkUCCa6AU/RUp2T1OMxe79wUa8Grg5V0E2n6GaAw2H72dZzipxioSSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:20.552021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74c0bbb0b5a40848194a8c45ac0e32de022c01c86eac62656b678f113e6559df","sha256:44acb4a7cb2049c10e31a45cf8798c7977168c8c9b8939ebfa766e4abec86bd9"],"state_sha256":"b530c5f52f8ee618cf664de1537abf26880f9a235fa7187b545c7bdef6d649e7"}