Properties of functions in the Wiener class BVp[a,b] for 0 < p < 1

We will investigate properties of functions in the wiener class bvp [a,b] with 0 < p < 1. we prove that any function in bvp [a,b] (0 < p < 1) can be expressed as the difference of two increasing functions in bvp [a,b]. we also obtain the explicit form of functions in bvp [a,b] and show that their derivatives are equal to zero a.e. on [a,b]. © 2015 yeli niu and heping wang.