We consider compact operators and integral equations in terms of integral kernels in the BVp 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.
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Boonpogkrong et al. (2024) studied this question.
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