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We consider Gaussian Besov spaces obtained by real interpolation andRiemann-Liouville operators of fractional integration on the Gaussian space andrelate the fractional smoothness of a functional to the regularity of its heatextension. The results are applied to study an approximation problem in $L_p$for $2\le p<\infty$ for stochastic integrals with respect to the$d$-dimensional (geometric) Brownian motion.

On fractional smoothness and $L_p$-approximation on the Gaussian space