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In this paper, the author prove that, the composite operator $T_1T_2$ satisfies the following estimate: for $\\lambda>0$ and weight $w\\in A_1(\\mathbb{R}^n)$, \\begin{eqnarray*}&&w\\big(\\{x\\in\\mathbb{R}^n:\\,|T_{1} T_2f(x)|>\\lambda\\}\\big)\\\\ &&\\quad\\lesssim [w]_{A_1}[w]_{A_{\\infty}}\\log ({\\rm e}+[w]_{A_{\\infty}}\\big) \\int_{\\mathbb{R}^n}\\frac{|f(x)|}{\\lambda}\\log \\Big({\\rm e}+\\frac{|f(x)|}{\\lambda}\\Big)w(x)dx,\\nonumber \\end{eqnarray*} and the composite operator $","authors_text":"Guoen Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-01T11:18:47Z","title":"Weighted weak type endpoint estimates for the composition of Calderon-Zygmund operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00289","kind":"arxiv","version":4},"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":"sha256:51d24d538f8cdb840e637ccee081847b4ffbe4c4bf064b6d4cdf6eff84e74f54","target":"record","created_at":"2026-05-18T00:09:52Z","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":"0a2580e0e814d1c51a6ee01085f34a32c9cf089e4e069a67811d56ec258cec3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-06-01T11:18:47Z","title_canon_sha256":"af9649972bba3e49c4d4eb80f9861d994d6bcb56ae64698f2f8486d3059e207c"},"schema_version":"1.0","source":{"id":"1806.00289","kind":"arxiv","version":4}},"canonical_sha256":"9d479dfde69aec3cedd881b7647f32861fe55c92773f144d7451d5c3f31c352a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d479dfde69aec3cedd881b7647f32861fe55c92773f144d7451d5c3f31c352a","first_computed_at":"2026-05-18T00:09:52.215477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:52.215477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8kBt0l/DrnuDy5xJ11XO4yzqtSn87HAvmTiV4AjXASJEvzeq9nraFLg1O4B26lT/xnN+eyrzSVdWnvNFgkWsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:52.216162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00289","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51d24d538f8cdb840e637ccee081847b4ffbe4c4bf064b6d4cdf6eff84e74f54","sha256:a637a2dac2ca9ba4e0f054a1fb9d983c02e1037499963274a010b4990f86b7fc"],"state_sha256":"618dc81e6a5b706e1e0c1ae9f78b3e2d740b5c3faeac87e21689f00e18ec2a74"}