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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 4, 1993, pp. 663–676
DOI: 10.4171/ZAA/539

Published online: 1993-12-31

Weakly Singular Hammerstein-Volterra Operators in Orlicz and Hölder Spaces

Jürgen Appell[1] and Martin Väth[2]

(1) Universität Würzburg, Germany
(2) Czech Academy of Sciences, Prague, Czech Republic

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.

Keywords: Hammerstein-Volterra operators, weakly singular kernels, strong nonhnearilies. fractional derivatives, Orlicz spaces, Hölder spaces

Appell Jürgen, Väth Martin: Weakly Singular Hammerstein-Volterra Operators in Orlicz and Hölder Spaces. Z. Anal. Anwend. 12 (1993), 663-676. doi: 10.4171/ZAA/539