Some sufficient conditions for compactness of linear Hammerstein integral operators and applications. (English) Zbl 1494.45017
The paper is concerned with the study of integral kernel operators on \(L^{p}(\Omega )\), where \(\Omega \) is a measurable subset of \(\mathbb{R}^{n}\). The main goal of the paper is to generalize existing sufficient conditions for such operators to map \(L^{p}(\Omega )\) into the space \(C(D)\) of continuous functions on a bounded closed set \(D\subseteq \Omega \), and to be compact. These conditions are expressed in terms of continuity and “sequential dominatedness” of the kernels.
Reviewer: Sophie Grivaux (Villeneuve d’Ascq)
MSC:
| 45P05 | Integral operators |
| 28A25 | Integration with respect to measures and other set functions |
| 47B38 | Linear operators on function spaces (general) |
Keywords:
integral kernel operators; linear Hammerstein integral operator; compactness; continuity under integral sign; sequential continuity; sequential dominatedness; sequential uniform continuityReferences:
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