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By a pointwise estimate for $\\|\\{T_Af_k(x)\\}\\|_{l^q}$ and the weighted $L^p$ estimates for the sparse operator $$\\mathcal{A}_{\\mathcal{S},\\,L(\\log L)^\\beta}f(x)=\\sum_{"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.07830","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-25T07:36:24Z","cross_cats_sorted":[],"title_canon_sha256":"9dc14b2dcc94ec06ee5dfac16d14c95b1cc80dc11a66171397403ec7b8fbb912","abstract_canon_sha256":"dfbaa9a307064f4156741cd71c3d2eaa5b4a37fdd155181ec449a51c9b7e50ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:48.960352Z","signature_b64":"tpA8qkj3Zjmi65465pa1OOd1wjrsxon1bHtYE5PqruDj/VGbVVfb6g5KcQpZRPuYLw6JT4fy236mUrxqxK1QCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e49bf119ef5671c0b88b7b774345f879b9b6adce5166fb66c95e43abd1ba8ede","last_reissued_at":"2026-05-18T00:35:48.959878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:48.959878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted vector-valued estimates for a non-standard Calder\\'on-Zygmund operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoen Hu","submitted_at":"2016-02-25T07:36:24Z","abstract_excerpt":"In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\\rm p.\\,v.}\\int_{\\mathbb{R}^n}\\frac{\\Omega(x-y)}{|x-y|^{n+1}}\\big(A(x)-A(y)-\\nabla A(y)\\big)f(y){\\rm d}y,$$ and the corresponding maximal operator $T_A^*$, where $\\Omega$ is homogeneous of degree zero, has vanishing moment of order one, $A$ is a function in $\\mathbb{R}^n$ such that $\\nabla A\\in {\\rm BMO}(\\mathbb{R}^n)$. 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