Extensions of functional LIL w.r.t. (r, p)--Capacities on Wiener space

Let {wt, t[greater-or-equal, slanted]0} be a d-dimensional Brownian motion and , 0[less-than-or-equals, slant]s[less-than-or-equals, slant]1, where . Let [gamma]:R+-->R. Under suitable conditions on [gamma], we generalize here functional law of the iterated logarithm (LIL) of Chung type to capacity Cr,p, that the limit set of [gamma](t)[xi]t(·) as t-->[infinity] exists and is determined in a Hölderian topology or uniform topology w.r.t. capacity Cr,p-q.e. on Wiener space. A functional LIL of Strassen type in Hölder norm w.r.t. Cr,p is also derived.