Generalized fractional smoothness and LpLp-variation of BSDEs with non-Lipschitz terminal condition

We relate the LpLp-variation, 2≤p<∞2≤p<∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.