Acting, boundedness, and compactness conditions for nonlinear Hanimerstein- Vol terra operators are given either between two Orlicz spaces, or from an Orlicz space into a (generalized) Hölder space. Particular emphasis is put on weakly singular kernels. This leads to (local) solvability results for Hammerstein-Volterra equations of second kind.
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Jürgen Appell, Martin Väth, Weakly Singular Hammerstein-Volterra Operators in Orlicz and Hölder Spaces. Z. Anal. Anwend. 12 (1993), no. 4, pp. 663–676DOI 10.4171/ZAA/539