In this paper, we obtained a necessary and sufficient condition for the embedding H ω q ([0, 1]) ⊂ IBV q p ([0, 1]), where IBV q p denotes the set of functions of bounded q-integral p-variation. Additionally, the conditions for the composition and superposition operators were provided to map the space H ω q ([0, 1]) into itself, by which these operators were bounded. Finally, we applied these results to examine the existence and uniqueness of solutions to Hammerstein integral equations in the space of H ω q ([0, 1]).