Fractional smoothness for the generalized local time of the indefinite Skorohod integral

Let be the indefinite Skorohod integral on Wiener space (Ω,H,P), and let Lt(x) be its the generalized local time introduced by Tudor in [C.A. Tudor, Martingale-type stochastic calculus for anticipating integral processes, Bernoulli 10 (2004) 313–325]. We prove that the generalized local time, as a nonlinear functional of ω, is in the fractional Sobolev spaces Dα,p ( and p>2) under some conditions imposed on the anticipating integrand u via the technique of Malliavin calculus and the K-method in the real interpolation theory. The result is optimal for the fractional Brownian motion with the Hurst parameter .