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We prove that for all 0<p<\\infty there exists a constant C, depending only on p and E, such that for all T \\geq 0 we have \\E \\sup_{0\\le t\\le T} || \\int_0^t e^{(t-s)A} g_s dW_s \\ ||^p \\leq C \\mathbb{E} (\\int_0^T || g_t ||_{\\gamma(H,E)}^2 dt)^\\frac{p}{2}. For p \\geq 2 the proof is based on 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":"1105.4720","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-24T10:10:14Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"ae158c79806639cf4e6db7c5d5d04bfc4c9d5b6d2b27c23539ba3282165ccbc5","abstract_canon_sha256":"f57c9a65d6ea7da6314d2f48ef7e6f9fd12d53a44f7b52978943c3c482d87170"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:23.405595Z","signature_b64":"dHKlp5EnMNVzyJ0wgyOPgxLzSWRJ745B44D4XE9kwVGICekZ18Tsg74gqxHBwm7bS7AVSxvqy74HG4LowYnTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed5054de3785770d3f29a9da9de410b1385a0391b5b89d4118f57250dd87e587","last_reissued_at":"2026-05-18T04:10:23.405080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:23.405080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A maximal inequality for stochastic convolutions in 2-smooth Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Jan van Neerven, Jiahui Zhu","submitted_at":"2011-05-24T10:10:14Z","abstract_excerpt":"Let (e^{tA})_{t \\geq 0} be a C_0-contraction semigroup on a 2-smooth Banach space E, let (W_t)_{t \\geq 0} be a cylindrical Brownian motion in a Hilbert space H, and let (g_t)_{t \\geq 0} be a progressively measurable process with values in the space \\gamma(H,E) of all \\gamma-radonifying operators from H to E. We prove that for all 0<p<\\infty there exists a constant C, depending only on p and E, such that for all T \\geq 0 we have \\E \\sup_{0\\le t\\le T} || \\int_0^t e^{(t-s)A} g_s dW_s \\ ||^p \\leq C \\mathbb{E} (\\int_0^T || g_t ||_{\\gamma(H,E)}^2 dt)^\\frac{p}{2}. 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