Multivalued superposition operators in ideal spaces of vector functions. I (Q1192446)

The paper is concerned with boundedness properties of nonlinear superposition operators generated by multivalued functions \(f: \Omega\times\mathbb{R}^ m\to{\mathcal P}(\mathbb{R}^ n)\) between ideal spaces ( Banach lattices) of vector functions. In particular, sufficient conditions on the spaces \(X\) and \(Y\) are given under which any superposition operator from \(X\) into \({\mathcal P}(Y)\) is locally bounded or bounded on bounded sets.