On fractional smoothness and Lp-approximation on the Gaussian space

We consider Gaussian Besov spaces obtained by real interpolation and Riemann.Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension.The results are applied to study an approximation problem in Lp for 2.p<. for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.