On the superposition operator in the space of functions of Hqw([0,1])

In this paper, we obtained a necessary and sufficient condition for the embedding Hq omega ([0, 1]) c IBVpq ([0, 1]), where IBVpq 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 Hq omega ([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 Hq omega ([0, 1]).