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Upper moment bounds and maximal upper moment bounds are obtained for Wiener integrals considered with respect to a fractional Brownian motion with Hurst index H < 1/2. Maximal bounds are derived from new maximal inequalities for Gaussian random variables and stochastic processes. 2000 Mathematics Subject Classification. Primary 60G15, 60H05.doi:10.1090/s0094-9000-08-00713-8 fatcat:zngoj7zhtfglvk54fj2m7fqm6q