Abstract
In this paper, we obtained a necessary and sufficient condition for the embedding H?q([0,1])? IBVqp([0,1]), where IBVq 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?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?q([0,1]).
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