{"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}. For p \\geq 2 the proof is based on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4720","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}