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We prove for $n\\ge 2$ that $M$ defines an operator bounded on $L^p(H^n)$ provided that $p>2n/(2n-1)$. This improves an earlier result by Nevo and Thangavelu, and the range for $L^p$ boundedness is optimal. We also extend the result to a more general setting of surfaces and to groups satisfying a nondegeneracy condition; these include the groups of Heisenberg type."},"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":"math/0307042","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2003-07-03T08:54:58Z","cross_cats_sorted":[],"title_canon_sha256":"042542d25e46188678aca8d50fabc3c10e3a1c6fa32d6cf82dd77271ed0eba4a","abstract_canon_sha256":"9b0fd278c6a6cd86e4ccf49e0fd40ff517c7be2362292b0e5ae63c4309dc2f49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:23:15.208174Z","signature_b64":"90d5bz/XDYTc0LVLhajVHMa021HUamCxVWeKXxgjRdwuJQ/Kj9baZ/swuTWKwGsF3/nagoUUebUpQKzK3vUIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1228c3dccab1f6dea0e7ab51297ce832ccbf8a19d777df1ae631977671d326fa","last_reissued_at":"2026-07-04T17:23:15.207763Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:23:15.207763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular spherical maximal operators on a class of two step nilpotent Lie groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Detlef Mueller","submitted_at":"2003-07-03T08:54:58Z","abstract_excerpt":"Let $H^n\\cong \\Bbb R^{2n}\\ltimes \\Bbb R$ be the Heisenberg group and let $\\mu_t$ be the normalized surface measure for the sphere of radius $t$ in $\\Bbb R^{2n}$. Consider the maximal function defined by $Mf=\\sup_{t>0} |f*\\mu_t|$. We prove for $n\\ge 2$ that $M$ defines an operator bounded on $L^p(H^n)$ provided that $p>2n/(2n-1)$. This improves an earlier result by Nevo and Thangavelu, and the range for $L^p$ boundedness is optimal. 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