COMPACT OPERATORS AND INTEGRAL EQUATIONS IN THE BVp SPACE

Abstract

We consider compact operators and integral equations in terms of integral kernels in the $B{V}_p$ space, the space of all bounded $p$-variation on a compact interval. The integral used in this paper is of Stieltjes type. The integral is an integration with respect to a function of bounded $p$-variation. A fractional Brownian motion in the stochastic integral is a processes of bounded $p$-variation.