Geodesic
On the Aronszajn property for integral equations in Banach space
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 83 (1989) no. 1, pp. 93-99

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Zbl MR
For the integral equation (1) below we prove the existence on an interval $J = [0, a]$ of a solution $x$ with values in a Banach space $E$, belonging to the class $L^{p}(J,E)$, $p>1$. Further, the set of solutions is shown to be a compact one in the sense of Aronszajn. 
Szufla, Stanisław. On the Aronszajn property for integral equations in Banach space. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 83 (1989) no. 1, pp. 93-99. http://geodesic.mathdoc.fr/item/RLINA_1989_8_83_1_a15/
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