Smoothness of local times of semimartingales

In this paper, applying the K-method in the real interpolation theory we sh ow that for some semimartingales, their local times considered as functiona ls on the Wiener space belong to the fractional Sobolev spaces on the Wiene r space D-alpha(p) for p > 1 and alpha < 1/2. Moreover, for the Brownian mo tion, we can prove that the result for the regularity of the local time as a functional on the Wiener space is optimal. (C) 2000 Academie des sciences /Editions scientifiques et medicales Elsevier SAS.