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In particular, we show that, exactly as for the Hilbert transform, $\\|{\\mathcal C}\\|_{L^p(w)}$ is bounded linearly by $[w]_{A_q}$ for $1\\le q<p$.\n  We also obtain $L^p(w)$ bounds in terms of $[w]_{A_p}$, whose sharpness is related to certain conjectures (for instance, of Konyagin \\cite{K2}) on pointwise convergence of Fourier series for functions near $L^1$.\n  Our approach works in t"},"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":"1312.0833","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-03T14:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"adb9a76a8dd2710b203f2e6b3bbded127517afcad9a6871d3af4d645f001082d","abstract_canon_sha256":"6badee268bf4f403f7122209edb306974aeb819d6c92768ea0231dd7ea59184a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.297969Z","signature_b64":"E7Ecr98ZTG6J4matBI3dT6F8ZdYDynmsgXMyHZEyF7X0HGVdNLVsRRqPfmSjGggWItpx+kjF5y8DwZ0CSIgzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cb1c85f344da161c22777dab76ac6f4ea78341ce5ce1ce73049a3c14ce32550","last_reissued_at":"2026-05-18T00:44:29.297411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.297411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On weighted norm inequalities for the Carleson and Walsh-Carleson operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei K. 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