Some sufficient conditions for compactness of linear Hammerstein integral operators and applications (Q2125043)

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.