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This operator appears very naturally in the theory of bilinear operators such as the bilinear Calder\\'on-Zygmund operators, the bilinear Hardy-Littlewood maximal operator introduced by Calder\\'on or in the study of pseudodifferential operators. To this end, we need to study H\\\"older's inequality for Lorentz spaces with change of measures $$\n  \\Vert fg \\Vert_{L^{p,\\infty}\\left(w_1^{p/p_1} w_2^{p/p_2}\\right)} \\le C \\Vert f \\Vert_{L^{p_1,\\infty}(w_1 )} \\Vert g \\Vert_{"},"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":"1801.08302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-25T08:22:51Z","cross_cats_sorted":[],"title_canon_sha256":"2e0279f776e4d2aa02b09559a1b782a567503c334accdb93aa58de5e3e90b583","abstract_canon_sha256":"75b9b95c2fa8e4e2973a100c856a7d2675a7491c0ff4b3139a3bce9d7b26a809"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:06.591601Z","signature_b64":"Q5CWLazxXQwypYEJO0Nevtonykj7oPaSce0DgGcCzNtv4Kieyqsk+c0YkkjLsWLtiqOrvGy1I8PjaaqyyCncAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a1b98955c43740c4e0c19dec190e2ddfa1f429a3e4ee60cf423611a6adb690a","last_reissued_at":"2026-05-18T00:25:06.591220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:06.591220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted boundedness of the 2-fold product of Hardy-Littlewood maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eduard Roure, Mar\\'ia J. 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